A220892 G.f.: (1+8*x+22*x^2+8*x^3+x^4)/(1-x)^6.

1, 14, 91, 364, 1085, 2666, 5719, 11096, 19929, 33670, 54131, 83524, 124501, 180194, 254255, 350896, 474929, 631806, 827659, 1069340, 1364461, 1721434, 2149511, 2658824, 3260425, 3966326, 4789539, 5744116, 6845189, 8109010, 9552991, 11195744, 13057121, 15158254, 17521595, 20170956, 23131549

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

M. Hering and B. J. Howard, The ring of evenly weighted points on the line, arXiv:1211.3941 [math.AG], 2012-2014; See example 3.8.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = (n+1)*(n^2+3*n+3)*(n^2+n+1)/3. [Colin Barker, Jan 03 2013]

The formula is simpler if the offset is 1 rather than 0. For a(n) = b*(1+b^2+b^4)/3, b >= 1. - N. J. A. Sloane, Nov 12 2019

E.g.f.: exp(x)*(3 + 39*x + 96*x^2 + 66*x^3 + 15*x^4 + x^5)/3. - Stefano Spezia, Dec 22 2021

Mathematica

CoefficientList[Series[(1+8x+22x^2+8x^3+x^4)/(1-x)^6, {x, 0, 40}], x] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 14, 91, 364, 1085, 2666}, 40] (* Harvey P. Dale, Jan 11 2020 *)

Prog

(PARI) a(n)=n*(9+13*n+11*n^2+5*n^3+n^4)/3+1 \\ Charles R Greathouse IV, Jan 03 2013

Crossrefs

Cf. A220893.

Sequence in context: A047639 A202291 A010930 * A022609 A060217 A113776

Adjacent sequences: A220889 A220890 A220891 * A220893 A220894 A220895

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 30 2012

Status

approved