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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
 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, 412, 157, 2, 2, 393, 704, 980, 1079, 812, 402, 2, 2, 1124, 1826, 1684, 2788, 2620, 1943, 1133, 2, 2, 3313, 5137, 3510, 6659, 7595, 4563, 5263, 3322, 2, 2, 9876, 15011, 8647 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums: {2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098,...}. LINKS FORMULA p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2))). EXAMPLE {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, 412, 157, 2}, {2, 393, 704, 980, 1079, 812, 402, 2}, {2, 1124, 1826, 1684, 2788, 2620, 1943, 1133, 2}, {2, 3313, 5137, 3510, 6659, 7595, 4563, 5263, 3322, 2}, {2, 9876, 15011, 8647, 10169, 20815, 18719, 9826, 15146, 9885, 2} MATHEMATICA Clear[p, n, m, x]; p[x, 0] = 2; p[x, 1] = 3*x + 3; p[x, 2] = 2*x^2 + 14*x + 2; p[x_, n_] := p[x, n] = (x + 1)*(p[x, n - 1] + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2))); Table[ExpandAll[p[x, n]], {n, 0, 10}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A338307 A153290 A153516 * A153312 A153283 A153288 Adjacent sequences:  A153308 A153309 A153310 * A153312 A153313 A153314 KEYWORD nonn,uned,tabl AUTHOR Roger L. Bagula, Dec 23 2008 STATUS approved

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Last modified May 5 19:23 EDT 2021. Contains 343573 sequences. (Running on oeis4.)