A190737 Diagonal sums of the Riordan matrix A104259.

1, 2, 6, 19, 66, 244, 946, 3801, 15697, 66234, 284339, 1237983, 5453611, 24263355, 108865901, 492051006, 2238220336, 10238568080, 47070014643, 217363784060, 1007794226777, 4689545704246, 21893712581740, 102520882301832, 481393173378979

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: (1-x-2*x^2-sqrt(1-6*x+5*x^2))/(2*x*(1-2*x+x^2+x^3)).

Recurrence: 0 = (n^2+17*n+72)*a(n+8) - (11*n^2+169*n+648)*a(n+7) + 3*(17*n^2+227*n+758)*a(n+6) - 2*(73*n^2+812*n+2259)*a(n+5)

+ 6*(41*n^2+375*n+846)*a(n+4) - (217*n^2+1559*n+2634)*a(n+3) + 3*(17*n^2+29*n-136)*a(n+2) + 10*(5*n^2+43*n+84)*a(n+1) - 25*(n^2+5*n+6)*a(n).

D-finite with recurrence: (n+1)*a(n) +(-8*n+1)*a(n-1) +3*(6*n-5)*a(n-2) +3*(-5*n+8)*a(n-3) +(-n-7)*a(n-4) +5*(n-2)*a(n-5)=0. - R. J. Mathar, Feb 24 2020

Mathematica

CoefficientList[Series[(1-x-2x^2-Sqrt[1-6x+5x^2])/(2x(1-2x+x^2+x^3)), {x, 0, 24}], x]

Prog

(PARI) x='x+O('x^30); Vec((1-x-2*x^2-sqrt(1-6*x+5*x^2))/(2*x*(1-2*x +x^2 +x^3))) \\ G. C. Greubel, Apr 23 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x-2*x^2-Sqrt(1-6*x+5*x^2))/(2*x*(1-2*x+x^2+x^3)))); // G. C. Greubel, Apr 23 2018

Crossrefs

Cf. A104259

Sequence in context: A150089 A150090 A150091 * A150092 A150093 A150094

Adjacent sequences: A190734 A190735 A190736 * A190738 A190739 A190740

Keyword

nonn

Author

Emanuele Munarini, May 18 2011

Status

approved