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A172099 Coefficients of polynomial recursion with powers n^2-1: p(x, n) = x^(2*n - 1)*p(x, n - 1) + p(x, n - 2) 0
1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,45

COMMENTS

Row sums are:

{1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,...}.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

p(x, n) = x^(2*n - 1)*p(x, n - 1) + p(x, n - 2)

EXAMPLE

{1},

{1, 1},

{1, 0, 0, 1, 1},

{1, 1, 0, 0, 0, 1, 0, 0, 1, 1},

{1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1},

{1, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1},

{1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1},

{1, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 2, 3, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1},

{1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 2, 3, 0, 0, 1, 3, 0, 0, 2, 3, 0, 0, 2, 3, 0, 0, 2, 3, 0, 0, 2, 3, 0, 0, 2, 3, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1}, {1, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 3, 0, 0, 2, 3, 0, 0, 3, 4, 0, 0, 2, 4, 0, 0, 3, 5, 0, 0, 2, 4, 0, 0, 3, 4, 0, 0, 2, 4, 0, 0, 3, 4, 0, 0, 2, 3, 0, 0, 2, 3, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1},

{1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 2, 3, 0, 0, 2, 4, 0, 0, 2, 4, 0, 0, 3, 5, 0, 0, 3, 5, 0, 0, 4, 6, 0, 0, 4, 6, 0, 0, 4, 6, 0, 0, 3, 6, 0, 0, 4, 6, 0, 0, 3, 5, 0, 0, 3, 5, 0, 0, 3, 5, 0, 0, 3, 4, 0, 0, 2, 3, 0, 0, 2, 3, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1}

MATHEMATICA

Clear[p, x, n, a];

p[x, 0] = 1; p[x, 1] = x + 1;

p[x_, n_] := p[x, n] = x^(2*n - 1)*p[x, n - 1] + p[x, n - 2];

a = Table[CoefficientList[p[x, n], x], {n, 0, 10}];

Flatten[a]

CROSSREFS

Sequence in context: A056137 A332602 A306383 * A170957 A178725 A257402

Adjacent sequences:  A172096 A172097 A172098 * A172100 A172101 A172102

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Jan 25 2010

STATUS

approved

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Last modified July 29 01:02 EDT 2021. Contains 346340 sequences. (Running on oeis4.)