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A174794
a(0) = 0 and a(n) = (4*n^3 - 12*n^2 + 20*n - 9)/3 for n >= 1.
5
0, 1, 5, 17, 45, 97, 181, 305, 477, 705, 997, 1361, 1805, 2337, 2965, 3697, 4541, 5505, 6597, 7825, 9197, 10721, 12405, 14257, 16285, 18497, 20901, 23505, 26317, 29345, 32597, 36081, 39805, 43777, 48005, 52497, 57261, 62305, 67637, 73265, 79197, 85441, 92005, 98897
OFFSET
0,3
COMMENTS
For n >= 1, a(n+1) = (4*n^3 + 8*n + 3)/3 is the number of evaluation points on the n-dimensional cube in Stenger's degree 7 cubature rule. - Franck Maminirina Ramaharo, Dec 18 2018
LINKS
Ronald Cools, Monomial cubature rules since "Stroud": a compilation - part 2, Journal of Computational and Applied Mathematics - Numerical evaluation of integrals Vol. 112 (1999), 21-27.
Ronald Cools and Philip Rabinowitz, Monomial cubature rules since "Stroud": a compilation, Journal of Computational and Applied Mathematics Vol. 48 (1993), 309-326.
Paul Pichler, Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method, Journal of Economic Dynamics and Control Vol. 35 (2011), 240-251.
FORMULA
G.f.: x*(1 + x)*(1 + 3*x^2)/(1 - x)^4.
From Franck Maminirina Ramaharo, Dec 17 2018: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n >= 5.
a(n) = 8*binomial(n - 1, 3) + 8*binomial(n - 1, 2) + 4*binomial(n - 1, 1) + 1, n >= 1.
E.g.f.: (9 - (9 - 12*x - 4*x^3)*exp(x))/3. (End)
MATHEMATICA
CoefficientList[Series[x*(1 + x)*(1 + 3*x^2)/(1 - x)^4, {x, 0, 50}], x]
PROG
(Maxima) a[0] : 0$ a[n] := (4*n^3 - 12*n^2 + 20*n - 9)/3$ makelist(a[n], n, 0, 50); /* Martin Ettl, Oct 21 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Mar 29 2010
EXTENSIONS
Definition replaced by polynomial - The Assoc. Eds. of the OEIS, Aug 10 2010
STATUS
approved