A322595 a(n) = (n^3 + 9*n + 14*n + 9)/3.
3, 11, 21, 35, 55, 83, 121, 171, 235, 315, 413, 531, 671, 835, 1025, 1243, 1491, 1771, 2085, 2435, 2823, 3251, 3721, 4235, 4795, 5403, 6061, 6771, 7535, 8355, 9233, 10171, 11171, 12235, 13365, 14563, 15831, 17171, 18585, 20075, 21643, 23291, 25021, 26835
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Ronald Cools, Encyclopaedia of Cubature Formulas
- 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.
- Srebra B. Stoyanova, Cubature of the seventh degree of accuracy for the hypersphere, Journal of Computational and Applied Mathematics Vol. 84 (1997), 15-21.
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[(n^3 + 9*n + 14*n + 9)/3: n in [0..45]]; // Vincenzo Librandi, Jun 05 2019
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Mathematica
Table[(n^3 + 9*n + 14*n + 9)/3, {n, 0, 50}] LinearRecurrence[{4,-6,4,-1},{3,11,21,35},50] (* Harvey P. Dale, Aug 19 2020 *) -
Maxima
makelist((n^3 + 9*n + 14*n + 9)/3, n, 0, 50);
Formula
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n >= 4.
a(n) = 2*binomial(n + 1, 3) + 6*binomial(n + 1, 2) + 2*binomial(n + 1, 1) + 1.
G.f.: (3 - x - 5*x^2 + 5*x^3)/(1 - x)^4. [Corrected by Georg Fischer, May 23 2019]
E.g.f.: (1/3)*(9 + 24*x + 12*x^2 + x^3)*exp(x).
Comments