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A321124 a(n) =  (4*n^3 - 6*n^2 + 14*n + 3)/3. 3
1, 5, 13, 33, 73, 141, 245, 393, 593, 853, 1181, 1585, 2073, 2653, 3333, 4121, 5025, 6053, 7213, 8513, 9961, 11565, 13333, 15273, 17393, 19701, 22205, 24913, 27833, 30973, 34341, 37945, 41793, 45893, 50253, 54881, 59785, 64973, 70453, 76233, 82321, 88725 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n >= 5, a(n) is the number of evaluation points on the n-dimensional cube in Phillips-Dobrodeev's degree 7 cubature rule.

LINKS

Table of n, a(n) for n=0..41.

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.

Ronald Cools and Philip Rabinowitz, Monomial cubature rules since "Stroud": a compilation, Journal of Computational and Applied Mathematics Vol. 48 (1993), 309-326.

L. N. Dobrodeev, Cubature formulas of the seventh order of accuracy for a hypersphere and a hypercube, USSR Computational Mathematics and Mathematical Physics Vol. 10 (1970), 252-253.

G. M. Phillips, Numerical integration over an N-dimensional rectangular region, The Computer Journal Vol. 10 (1967), 297-299.

Rudolf M. Schürer, High-Dimensional Numerical Integration on Parallel Computers, Phd Dissertation, 2001. p. 80.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 8*binomial(n, 3) + 4*binomial(n, 2) + 4*binomial(n, 1) + 1.

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

a(n) = a(n-1) + A128445(n+1), n >= 1.

E.g.f.: (1/3)*(3 + 12*x + 6*x^2 + 4*x^3)*exp(x).

G.f.: (1 + x - x^2 + 7*x^3)/(1 - x)^4.

MATHEMATICA

Table[(4*n^3 - 6*n^2 + 14*n + 3)/3, {n, 0, 50}]

PROG

(Maxima) makelist((4*n^3 - 6*n^2 + 14*n + 3)/3, n, 0, 50);

CROSSREFS

Cf. A000292, A128445, A161680, A174794, A322594, A322595.

Sequence in context: A272161 A272828 A308812 * A001981 A141025 A100227

Adjacent sequences:  A321121 A321122 A321123 * A321125 A321126 A321127

KEYWORD

nonn,easy

AUTHOR

Franck Maminirina Ramaharo, Dec 17 2018

STATUS

approved

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Last modified July 30 07:55 EDT 2021. Contains 346348 sequences. (Running on oeis4.)