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 A155120 2*(n^3+n^2+n-1). 3
 -2, 4, 26, 76, 166, 308, 514, 796, 1166, 1636, 2218, 2924, 3766, 4756, 5906, 7228, 8734, 10436, 12346, 14476, 16838, 19444, 22306, 25436, 28846, 32548, 36554, 40876, 45526, 50516, 55858 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Next level down in the triangle from A142463 =f[n]. {{1}, {1, 1}, {1, 2*n, 1}, {1, f[n], f[n], 1}, {1, g[n], 6 + 24 *(n - 1) + 28*(n - 1)^2 + 8* ( n - 1)^3, g[n], 1}, {1, h[n], k[n - 1] - h[n] - 1, k[n - 1] - h[n] - 1, h[n], 1}} f[n_]=3*n^2 - (n - 1)^2; g[n_]=-2 + 2 *n + 2* n^2 + 2 n^3; h[n_]=-3 + 2 n + 2 n^2 + 2 n^3 + 2*n^4; k[n_]=16+ 80 n + 140 *n^2 + 100*n^3 + 24* n^4; These functions and the triangles they make are general Pascal-Sierpinski functions. [What is the definition or principle of construction of this triangle and its polynomials? R. J. Mathar, Dec 15 2010] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..2000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 2*(n^3+n^2+n-1). G.f.: 2*(-1+6*x-x^2+2*x^3)/(x-1)^4. MATHEMATICA Table[ -2 + 2 n + 2 n^2 + 2 n^3, {n, 0, 30}] LinearRecurrence[{4, -6, 4, -1}, {-2, 4, 26, 76}, 40] (* Harvey P. Dale, Jun 06 2014 *) PROG (MAGMA) [2*(n^3+n^2+n-1): n in [0..40] ]; // Vincenzo Librandi, May 23 2011 CROSSREFS Cf. A142463, A155121 - A155124. Sequence in context: A129894 A028386 A259374 * A144691 A085700 A087404 Adjacent sequences:  A155117 A155118 A155119 * A155121 A155122 A155123 KEYWORD sign,easy AUTHOR Roger L. Bagula, Jan 20 2009 STATUS approved

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