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

0,3

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).

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)

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 *)

Prog

(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

Crossrefs

Sequence in context: A068012 A261930 A019138 * A338218 A001630 A293363

Adjacent sequences: A154321 A154322 A154323 * A154325 A154326 A154327

Keyword

nonn,easy

Author

Paul Barry, Jan 07 2009

Status

approved