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A171145 The sequence of coefficients of a polynomial recursion: p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + n*x + 1)^Floor[n/2]].

%I A171145 #3 Oct 09 2012 03:52:24
%S A171145 1,1,1,1,3,1,1,4,4,1,1,10,27,10,1,1,11,37,37,11,1,1,21,150,385,150,21,
%T A171145 1,1,22,171,535,535,171,22,1,1,36,490,3024,7539,3024,490,36,1,1,37,
%U A171145 526,3514,10563,10563,3514,526,37,1,1,55,1215,13530,76845,188001,76845
%N A171145 The sequence of coefficients of a polynomial recursion: p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + n*x + 1)^Floor[n/2]].
%C A171145 Row sums are:
%C A171145 {1, 2, 5, 10, 49, 98, 729, 1458, 14641, 29282, 371293, 742586,...}.
%C A171145 The modulo 2 of this appears to be a staggered Sierpinski-type fractal.
%F A171145 p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + n*x + 1)^Floor[n/2]]
%e A171145 {1},
%e A171145 {1, 1},
%e A171145 {1, 3, 1},
%e A171145 {1, 4, 4, 1},
%e A171145 {1, 10, 27, 10, 1},
%e A171145 {1, 11, 37, 37, 11, 1},
%e A171145 {1, 21, 150, 385, 150, 21, 1},
%e A171145 {1, 22, 171, 535, 535, 171, 22, 1},
%e A171145 {1, 36, 490, 3024, 7539, 3024, 490, 36, 1},
%e A171145 {1, 37, 526, 3514, 10563, 10563, 3514, 526, 37, 1},
%e A171145 {1, 55, 1215, 13530, 76845, 188001, 76845, 13530, 1215, 55, 1},
%e A171145 {1, 56, 1270, 14745, 90375, 264846, 264846, 90375, 14745, 1270, 56, 1}
%t A171145 Clear[p, n, x, a]
%t A171145 p[x, 1] := 1;
%t A171145 p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, (x + 1)*p[x, n - 1], (x^2 + n*x + 1)^Floor[n/2]];
%t A171145 a = Table[CoefficientList[p[x, n], x], {n, 1, 12}];
%t A171145 Flatten[a]
%Y A171145 Cf. A051159, A169623, A007318, A171142, A171143
%K A171145 nonn,tabl
%O A171145 1,5
%A A171145 _Roger L. Bagula_ and _Gary W. Adamson_, Dec 04 2009