A322597 a(n) = (4*n^3 - 6*n^2 + 20*n + 3)/3.

1, 7, 17, 39, 81, 151, 257, 407, 609, 871, 1201, 1607, 2097, 2679, 3361, 4151, 5057, 6087, 7249, 8551, 10001, 11607, 13377, 15319, 17441, 19751, 22257, 24967, 27889, 31031, 34401, 38007, 41857, 45959, 50321, 54951, 59857, 65047, 70529, 76311, 82401, 88807

Offset: 0

Author

Franck Maminirina Ramaharo, Jan 23 2019

Keywords

• nonn
• easy

Comments

For n >= 2, a(n) gives the number of function evaluations for Dooren and Ridder's degree 5 and 7 cubature rule over an n-dimensional cube, with the exception of a(3) = 45 and a(4) = 97.

Links

• Ronald Cools, Encyclopaedia of Cubature Formulas
• Paul van Dooren and Luc de Ridder, An adaptive algorithm for numerical integration over an n-dimensional cube, Journal of Computational and Applied Mathematics, Vol. 2 (1976), 207-217.
• Alan C. Genz and Awais A. Malik, Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region, Journal of Computational and Applied Mathematics, Vol. 6 (1980), 295-302.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

First differences: 2*A093328.

Cf. A174794, A321124, A322594, A322595.

Programs

Maple

[(4*n^3-6*n^2+20*n+3)/3$n=0..50]; # Muniru A Asiru, Jan 23 2019

Mathematica

Table[(4*n^3 - 6*n^2 + 20*n + 3)/3, {n, 0, 50}]

Maxima

makelist((4*n^3 - 6*n^2 + 20*n + 3)/3, n, 0, 50);

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n >= 4.

G.f.: (1 + 3*x - 5*x^2 + 9*x^3)/((1 - x)^4).

E.g.f.: (1/3)*(3 + 18*x + 6*x^2 + 4*x^3)*exp(x).