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A153311 Coefficient triangle sequence of a polynomial recursion: p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2))); Row sums are 2*3^n. 0

%I

%S 2,3,3,2,14,2,2,25,25,2,2,36,77,45,2,2,65,167,176,74,2,2,148,313,424,

%T 412,157,2,2,393,704,980,1079,812,402,2,2,1124,1826,1684,2788,2620,

%U 1943,1133,2,2,3313,5137,3510,6659,7595,4563,5263,3322,2,2,9876,15011,8647

%N Coefficient triangle sequence of a polynomial recursion: p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2))); Row sums are 2*3^n.

%C Row sums:

%C {2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098,...}.

%F p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2))).

%e {2},

%e {3, 3},

%e {2, 14, 2},

%e {2, 25, 25, 2},

%e {2, 36, 77, 45, 2},

%e {2, 65, 167, 176, 74, 2},

%e {2, 148, 313, 424, 412, 157, 2},

%e {2, 393, 704, 980, 1079, 812, 402, 2},

%e {2, 1124, 1826, 1684, 2788, 2620, 1943, 1133, 2},

%e {2, 3313, 5137, 3510, 6659, 7595, 4563, 5263, 3322, 2},

%e {2, 9876, 15011, 8647, 10169, 20815, 18719, 9826, 15146, 9885, 2}

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

%t p[x, 0] = 2; p[x, 1] = 3*x + 3; p[x, 2] = 2*x^2 + 14*x + 2;

%t p[x_, n_] := p[x, n] = (x + 1)*(p[x, n - 1] + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2)));

%t Table[ExpandAll[p[x, n]], {n, 0, 10}];

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

%t Flatten[%]

%Y A025192

%K nonn,uned,tabl

%O 0,1

%A _Roger L. Bagula_, Dec 23 2008

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Last modified April 14 21:21 EDT 2021. Contains 342962 sequences. (Running on oeis4.)