A164854 Diagonal sum of generalized Pascal triangle; (10^n,1).

1, 1, 11, 12, 113, 125, 1138, 1263, 11401, 12664, 114065, 126729, 1140794, 1267523, 11408317, 12675840, 114084157, 126759997, 1140844154, 1267604151, 11408448305, 12676052456, 114084500761, 126760553217, 1140845053978, 1267605607195, 11408450661173

Offset: 0

Author

Mark Dols, Aug 28 2009

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..1990
• Index entries for linear recurrences with constant coefficients, signature (1,11,-10,-10).

Crossrefs

Cf. A164844, A164852, A000045.

Programs

Maple

f:= gfun:-rectoproc({10*a(n-4)+10*a(n-3)-11*a(n-2)-a(n-1)+a(n),
a(0)=1,a(1)=1,a(2)=11,a(3)=12},a(n),remember):
map(f, [$0..30]); # Robert Israel, Jul 01 2016

Mathematica

LinearRecurrence[{1,11,-10,-10},{1,1,11,12},30] (* Harvey P. Dale, Apr 07 2022 *)

Formula

From Robert Israel, Jul 01 2016: (Start)

G.f.: (1-x^2)/((1-10*x^2)*(1-x-x^2)).

a(n) = (171-9*(-1)^n)*10^floor(n/2)/142 + (A000045(n)-10*A000045(n+2))/71. (End)

a(n) = a(n-1)+11*a(n-2)-10*a(n-3)-10*a(n-4). - Wesley Ivan Hurt, Apr 21 2021

Extensions

More terms from Harvey P. Dale, Apr 07 2022