A089950 Partial sums of A001652.

0, 3, 23, 142, 838, 4897, 28557, 166460, 970220, 5654879, 32959075, 192099594, 1119638514, 6525731517, 38034750617, 221682772216, 1292061882712, 7530688524091, 43892069261871, 255821727047174, 1491038293021214, 8690408031080153, 50651409893459749

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-14,8,-1).

Formula

a(n) = Sum_{k=0...n} A001652(k).

a(n) = A000129(n+1)^2-floor((n+2)/2); e.g. 0=1^2-1 and 166460=408^2-4.

G.f.: -x*(-3+x) / ( (1-6*x+x^2)*(x-1)^2 ). - R. J. Mathar, Feb 05 2016

a(n) = (-6 + (3-2*sqrt(2))^(1+n) + 3*(3+2*sqrt(2))^n + 2*sqrt(2)*(3+2*sqrt(2))^n - 4*n) / 8. - Colin Barker, Aug 10 2018

Prog

(PARI) concat(0, Vec(-x*(-3+x)/((1-6*x+x^2)*(x-1)^2) + O(x^40))) \\ Michel Marcus, Feb 05 2016

Crossrefs

Sequence in context: A081413 A179328 A255952 * A198797 A057835 A232145

Adjacent sequences: A089947 A089948 A089949 * A089951 A089952 A089953

Keyword

nonn,easy

Author

Charlie Marion, Jan 11 2004

Status

approved