A259859 - OEIS

%I #31 Dec 26 2022 16:09:44

%S 0,1,3,10,38,177,999,6676,51564,451585,4418555,47746686,564528978,

%T 7247396065,100378220943,1491699317032,23673159231704,399553959924801,

%U 7146023007880179,134997604341408370,2686037319660797310,56143557248353416721,1229914413684635491703

%N a(0)=0; thereafter A003470(n-1) + A003470(n) - 1.

%H John Riordan and N. J. A. Sloane, <a href="/A003471/a003471_1.pdf">Correspondence, 1974</a>

%F D-finite with recurrence: (-n+2)*a(n) +(n-1)^2*a(n-1) +2*(-n+2)*a(n-2) +(-n^2+4*n-2)*a(n-3) +(n-1)*a(n-4)=0. - _R. J. Mathar_, Jul 15 2015

%p b:= proc(n) b(n):= `if`(n<2, 1, n*b(n-1)-b(n-2)+1+(-1)^n) end:

%p a:= n-> `if`(n=0, 0, b(n-1)+b(n)-1):

%p seq(a(n), n=0..22);  # _Alois P. Heinz_, Jun 17 2021

%t b[n_] := b[n] = If[n<2, 1, n*b[n-1] - b[n-2] + 1 + (-1)^n];

%t a[n_] := If[n == 0, 0, b[n-1] + b[n] - 1];

%t Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Dec 26 2022, after _Alois P. Heinz_ *)

%Y Cf. A003470.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jul 07 2015, based on a suggestion from _John Riordan_, Nov 14 1974.

%E Offset corrected by _N. J. A. Sloane_, Jun 16 2021