A259110 2*A000447(n).

0, 2, 20, 70, 168, 330, 572, 910, 1360, 1938, 2660, 3542, 4600, 5850, 7308, 8990, 10912, 13090, 15540, 18278, 21320, 24682, 28380, 32430, 36848, 41650, 46852, 52470, 58520, 65018, 71980, 79422, 87360, 95810, 104788, 114310, 124392, 135050, 146300, 158158, 170640, 183762, 197540, 211990, 227128, 242970

Offset: 0

Author

N. J. A. Sloane, Jun 24 2015

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• J. L. Bailey, Jr., A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359.
• J. L. Bailey, A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359. [Annotated scanned copy]
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000447.

Programs

Mathematica

LinearRecurrence[{4,-6,4,-1},{0,2,20,70},50] (* Harvey P. Dale, Feb 01 2018 *)

PARI

concat(0, Vec(2*x*(x^2+6*x+1)/(x-1)^4 + O(x^100))) \\ Colin Barker, Jun 28 2015

Formula

a(n) = (2*n*(4*n^2-1))/3. - Colin Barker, Jun 28 2015

G.f.: 2*x*(x^2+6*x+1) / (x-1)^4. - Colin Barker, Jun 28 2015

a(n) = 2*binomial(2*n+1, 3). - Michel Marcus, Mar 05 2022