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

Author

Paul Barry, Feb 27 2011

Keywords

• nonn
• easy

Programs

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 *)

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