OFFSET
0,2
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).
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).
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}]
PROG
(Maxima) makelist((4*n^3 - 6*n^2 + 20*n + 3)/3, n, 0, 50);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Franck Maminirina Ramaharo, Jan 23 2019
STATUS
approved