A154324 Diagonal sums of number triangle A113582.

1, 1, 2, 3, 6, 12, 23, 43, 74, 124, 195, 300, 441, 637, 890, 1226, 1647, 2187, 2848, 3673, 4664, 5874, 7305, 9021, 11024, 13390, 16121, 19306, 22947, 27147, 31908, 37348, 43469, 50405, 58158, 66879, 76570, 87400, 99371, 112671, 127302, 143472, 161183, 180664

Offset: 0

Author

Paul Barry, Jan 07 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-8,6,6,-8,0,3,-1).

Programs

Mathematica

LinearRecurrence[{3,0,-8,6,6,-8,0,3,-1}, {1,1,2,3,6,12,23,43,74}, 25] (* G. C. Greubel, Sep 11 2016 *)
CoefficientList[Series[(1 - 2 x - x^2 + 5 x^3 - x^4 - 2 x^5 + x^6) / ((1 - x) (1 - x^2))^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 12 2016 *)

PARI

Vec((1-2*x-x^2+5*x^3-x^4-2*x^5+x^6) / ((1-x)^6*(1+x)^3) + O(x^60)) \\ Colin Barker, Sep 12 2016

Formula

G.f.: (1 -2*x -x^2 +5*x^3 -x^4 -2*x^5 +x^6)/((1-x)*(1-x^2))^3.

a(n) = Sum_{k=0..floor(n/2)} ( 1 + C(k+1,2)*C(n-2k+1,2) ).

From Colin Barker, Sep 12 2016: (Start)

a(n) = (2895 + 945*(-1)^n + (1786-90*(-1)^n)*n - 30*(3+(-1)^n)*n^2 + 40*n^3 + 30*n^4 + 4*n^5)/3840.

a(n) = (2*n^5+15*n^4+20*n^3-60*n^2+848*n+1920)/1920 for n even.

a(n) = (2*n^5+15*n^4+20*n^3-30*n^2+938*n+975)/1920 for n odd. (End)