login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322594 a(n) = (4*n^3 + 12*n^2 - 4*n + 3)/3. 4
1, 5, 25, 69, 145, 261, 425, 645, 929, 1285, 1721, 2245, 2865, 3589, 4425, 5381, 6465, 7685, 9049, 10565, 12241, 14085, 16105, 18309, 20705, 23301, 26105, 29125, 32369, 35845, 39561, 43525, 47745, 52229, 56985, 62021, 67345, 72965, 78889, 85125, 91681, 98565 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) is the number of evaluation points on the n-dimensional cube in Lyness's degree 7 cubature rule.
REFERENCES
Arthur H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall, 1971.
LINKS
Ronald Cools and Philip Rabinowitz, Monomial cubature rules since "Stroud": a compilation, Journal of Computational and Applied Mathematics Vol. 48 (1993), 309-326.
James Lu and David L. Darmofal, Higher-dimensional integration with gaussian weight for applications in probabilistic design, SIAM J. Sci. Comput. Vol. 26 (2004), 613-624.
James N. Lyness, Symmetric integration rules for hypercubes II. Rule projection and rule extension, Math. Comp. Vol. 19 (1965), 394-407.
FORMULA
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n >= 5.
a(n) = a(n-1) + 4*A028387(n-1), n >= 1.
a(n) = 8*binomial(n, 3) + 16*binomial(n, 2) + 4*binomial(n, 1) + 1.
G.f.: (1 + x + 11*x^2 - 5*x^3)/(1 - x)^4
E.g.f.: (1/3)*(3 + 12*x + 24*x^2 + 4*x^3)*exp(x).
MATHEMATICA
Table[(4*n^3 + 12*n^2 - 4*n + 3)/3, {n, 0, 50}]
PROG
(Maxima) makelist((4*n^3 + 12*n^2 - 4*n + 3)/3, n, 0, 50);
CROSSREFS
Sequence in context: A018782 A340388 A146665 * A059302 A147130 A154286
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)