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A155120
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2*(n^3+n^2+n-1).
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3
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-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
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OFFSET
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0,1
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COMMENTS
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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]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = 2*(n^3+n^2+n-1).
G.f.: 2*(-1+6*x-x^2+2*x^3)/(x-1)^4.
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MATHEMATICA
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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 *)
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PROG
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(MAGMA) [2*(n^3+n^2+n-1): n in [0..40] ]; // Vincenzo Librandi, May 23 2011
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CROSSREFS
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Cf. A142463, A155121 - A155124.
Sequence in context: A129894 A028386 A259374 * A144691 A085700 A087404
Adjacent sequences: A155117 A155118 A155119 * A155121 A155122 A155123
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KEYWORD
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sign,easy
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AUTHOR
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Roger L. Bagula, Jan 20 2009
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STATUS
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approved
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