A186828 Diagonal sums of number triangle A186826.

1, 1, 4, 14, 57, 247, 1124, 5296, 25621, 126529, 635264, 3232886, 16638821, 86456767, 452927448, 2389672752, 12686560409, 67721774737, 363268546892, 1957131383342, 10585610149121, 57458399978455, 312890905815900, 1708883398754176, 9358483855106829, 51378142520487281, 282714583026982504

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

G.f.: (1+x-3x^2+x^3-(1+x^2)*sqrt(1-6x+x^2))/(4x(1-x+x^2+x^3)).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(9*n-7)*a(n-2) +(-13*n+36)*a(n-3) +(3*n-35)*a(n-4) +(-5*n+28)*a(n-5) +(-5*n+21)*a(n-6) +(n-6)*a(n-7)=0. - R. J. Mathar, Feb 13 2015

Mathematica

CoefficientList[Series[(1+x-3x^2+x^3-(1+x^2)Sqrt[1-6x+x^2])/(4x(1-x+ x^2+ x^3)), {x, 0, 30}], x] (* Harvey P. Dale, Aug 23 2011 *)

Crossrefs

Sequence in context: A002735 A026652 A269134 * A151489 A325929 A134826

Adjacent sequences: A186825 A186826 A186827 * A186829 A186830 A186831

Keyword

nonn,easy

Author

Paul Barry, Feb 27 2011

Status

approved