A322593 -id:A322593 - cp's OEIS frontend

2, 7, 17, 33, 57, 93, 149, 241, 401, 693, 1245, 2313, 4409, 8557, 16805, 33249, 66081, 131685, 262829, 525049, 1049417, 2098077, 4195317, 8389713, 16778417, 33555733, 67110269, 134219241, 268437081, 536872653, 1073743685, 2147485633, 4294969409, 8589936837

Offset: 0

Franck Maminirina Ramaharo, Dec 17 2018

For n >= 2, a(n) is the number of evaluation points on the n-dimensional cube in Genz and Malik's degree 7 cubature rule.

Marius A. Burtea, Table of n, a(n) for n = 0..201
Ronald Cools, Encyclopaedia of Cubature Formulas
Ronald Cools and Philip Rabinowitz, Monomial cubature rules since "Stroud": a compilation, Journal of Computational and Applied Mathematics Vol. 48 (1993), 309-326.
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 (5,-9,7,-2).

Cf. A000051, A000079, A001787, A001844, A002064, A005126, A058331, A100314, A131830, A100314, A132750, A176691, A322593.

[2^n + 2*n^2 + 2*n + 1: n in [0..33]]; // Marius A. Burtea, Dec 28 2018

Table[2^n + 2*n^2 + 2*n + 1, {n, 0, 50}]

makelist(2^n + 2*n^2 + 2*n + 1, n, 0, 50);

a(n) = A000079(n) + A001844(n).
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4), n >= 4.
G.f.: (2 - 3*x - 3*x^3)/((1 - 2*x)*(1 - x)^3).
E.g.f.: exp(2*x) + (1 + 4*x + 2*x^2)*exp(x).

cp's OEIS Frontend

A321123 a(n) = 2^n + 2n^2 + 2n + 1.

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