A190255 Diagonal sums of the Riordan matrix (g(x),x*g(x)), where g(x) = (1-x-sqrt(1-2*x-3*x^2-4*x^3))/(2*x^2*(1+x)) (A190252).

1, 1, 3, 7, 18, 48, 131, 365, 1034, 2968, 8615, 25243, 74565, 221807, 663869, 1997765, 6040894, 18345668, 55931289, 171121717, 525225943, 1616805005, 4990386995, 15441275375, 47887524320, 148826022290, 463433496815, 1445737785557, 4517857601552

Offset

0,3

Links

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

Formula

Recurrence: 0 = 6*(n^2+15*n+54)*a(n+6) - (7*n^2+93*n+314)*a(n+5) - (25*n^2+309*n+962)*a(n+4) - 2*(22*n^2+228*n+587)*a(n+3) - (31*n^2+264*n+566)*a(n+2) - 3*(5*n^2+28*n+40)*a(n+1) - 2*(2*n^2+9*n+10)*a(n).

G.f.: (1-x-2*x^2-sqrt(1-2*x-3*x^2-4*x^3))/(2*x^2*(2+x)).

D-finite with recurrence: 2*(n+3)*a(n) +3*(-n-1)*a(n-1) +(-8*n-3)*a(n-2) +(-11*n+12)*a(n-3) +2*(-2*n+3)*a(n-4)=0. - R. J. Mathar, Jun 14 2016

Mathematica

Rest[CoefficientList[Series[(1-x-2x^2-Sqrt[1-2x-3x^2-4x^3])/(2x^2(2+x)), {x, 0, 27}], x]]

Prog

(PARI) x='x+O('x^30); Vec((1-x-2*x^2-sqrt(1-2*x-3*x^2-4*x^3))/(2*x^2*(2+x))) \\ G. C. Greubel, Dec 26 2017

Crossrefs

Cf. A190252.

Sequence in context: A018029 A099483 A225034 * A218250 A267799 A218783

Adjacent sequences: A190252 A190253 A190254 * A190256 A190257 A190258

Keyword

nonn

Author

Emanuele Munarini, May 06 2011

Status

approved