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