Coefficients from sequence of ceil divisions
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I wanted to know if there exists a systematic elegant “closed form” formula for calculating numbers ${{s}_{i,j,left{ 1,2 right}}}(n) in {{mathbb{N}}^{*}},$
and also positive rational numbers ${{t}_{k,l}}(n)in {{mathbb{Q}}}~$ , for any $nin {{mathbb{N}}^{*}}$, of which the cases for $n=7$, $n=6$ and $n=3$ are exemplified in the figures below. I am also interested in knowing the maximum value of index $i$ as a function of $nin {{mathbb{N}}^{*}}$ and the maximum value of index $j$ as a function of $i$.
sequences-and-series discrete-mathematics recurrence-relations ceiling-function
asked Dec 6 '18 at 11:58
HS TQHS TQ
426
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add a comment |
$begingroup$
I wanted to know if there exists a systematic elegant “closed form” formula for calculating numbers ${{s}_{i,j,left{ 1,2 right}}}(n) in {{mathbb{N}}^{*}},$
and also positive rational numbers ${{t}_{k,l}}(n)in {{mathbb{Q}}}~$ , for any $nin {{mathbb{N}}^{*}}$, of which the cases for $n=7$, $n=6$ and $n=3$ are exemplified in the figures below. I am also interested in knowing the maximum value of index $i$ as a function of $nin {{mathbb{N}}^{*}}$ and the maximum value of index $j$ as a function of $i$.
sequences-and-series discrete-mathematics recurrence-relations ceiling-function
asked Dec 6 '18 at 11:58
HS TQHS TQ
426
$endgroup$
$begingroup$
The diagrams are useless. What are the definitions?
$endgroup$
– William Elliot
Dec 8 '18 at 2:58
add a comment |
$begingroup$
I wanted to know if there exists a systematic elegant “closed form” formula for calculating numbers ${{s}_{i,j,left{ 1,2 right}}}(n) in {{mathbb{N}}^{*}},$
and also positive rational numbers ${{t}_{k,l}}(n)in {{mathbb{Q}}}~$ , for any $nin {{mathbb{N}}^{*}}$, of which the cases for $n=7$, $n=6$ and $n=3$ are exemplified in the figures below. I am also interested in knowing the maximum value of index $i$ as a function of $nin {{mathbb{N}}^{*}}$ and the maximum value of index $j$ as a function of $i$.
sequences-and-series discrete-mathematics recurrence-relations ceiling-function
asked Dec 6 '18 at 11:58
HS TQHS TQ
426
$endgroup$
I wanted to know if there exists a systematic elegant “closed form” formula for calculating numbers ${{s}_{i,j,left{ 1,2 right}}}(n) in {{mathbb{N}}^{*}},$
and also positive rational numbers ${{t}_{k,l}}(n)in {{mathbb{Q}}}~$ , for any $nin {{mathbb{N}}^{*}}$, of which the cases for $n=7$, $n=6$ and $n=3$ are exemplified in the figures below. I am also interested in knowing the maximum value of index $i$ as a function of $nin {{mathbb{N}}^{*}}$ and the maximum value of index $j$ as a function of $i$.
sequences-and-series discrete-mathematics recurrence-relations ceiling-function
sequences-and-series discrete-mathematics recurrence-relations ceiling-function
asked Dec 6 '18 at 11:58
HS TQHS TQ
426
asked Dec 6 '18 at 11:58
HS TQHS TQ
426
asked Dec 6 '18 at 11:58
HS TQHS TQ
426
asked Dec 6 '18 at 11:58
HS TQHS TQ
426
asked Dec 6 '18 at 11:58
HS TQHS TQ
426
426
$begingroup$
The diagrams are useless. What are the definitions?
$endgroup$
– William Elliot
Dec 8 '18 at 2:58
add a comment |
$begingroup$
The diagrams are useless. What are the definitions?
$endgroup$
– William Elliot
Dec 8 '18 at 2:58
$begingroup$
The diagrams are useless. What are the definitions?
$endgroup$
– William Elliot
Dec 8 '18 at 2:58
$begingroup$
The diagrams are useless. What are the definitions?
$endgroup$
– William Elliot
Dec 8 '18 at 2:58
add a comment |
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$begingroup$
The diagrams are useless. What are the definitions?
$endgroup$
– William Elliot
Dec 8 '18 at 2:58