The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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. SchÃ¼rer, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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