login
Partial sums of A001652.
2

%I #10 Aug 10 2018 17:33:20

%S 0,3,23,142,838,4897,28557,166460,970220,5654879,32959075,192099594,

%T 1119638514,6525731517,38034750617,221682772216,1292061882712,

%U 7530688524091,43892069261871,255821727047174,1491038293021214,8690408031080153,50651409893459749

%N Partial sums of A001652.

%H Colin Barker, <a href="/A089950/b089950.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-14,8,-1).

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

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

%F G.f.: -x*(-3+x) / ( (1-6*x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Feb 05 2016

%F 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

%o (PARI) concat(0, Vec(-x*(-3+x)/((1-6*x+x^2)*(x-1)^2) + O(x^40))) \\ _Michel Marcus_, Feb 05 2016

%K nonn,easy

%O 0,2

%A _Charlie Marion_, Jan 11 2004