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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

%I

%S 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,

%T 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,

%U 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

%N Coefficients of polynomial recursion with powers n^2-1: p(x, n) = x^(2*n - 1)*p(x, n - 1) + p(x, n - 2)

%C Row sums are:

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

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

%e {1},

%e {1, 1},

%e {1, 0, 0, 1, 1},

%e {1, 1, 0, 0, 0, 1, 0, 0, 1, 1},

%e {1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1},

%e {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},

%e {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},

%e {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},

%e {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},

%e {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}

%t Clear[p, x, n, a];

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

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

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

%t Flatten[a]

%K nonn,uned

%O 0,45

%A _Roger L. Bagula_, Jan 25 2010

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Last modified September 23 12:20 EDT 2021. Contains 347617 sequences. (Running on oeis4.)