A115285 Diagonal sums of correlation triangle for 1,3,4,4,4,...(A113311).

1, 3, 7, 14, 23, 35, 50, 67, 87, 110, 135, 163, 194, 227, 263, 302, 343, 387, 434, 483, 535, 590, 647, 707, 770, 835, 903, 974, 1047, 1123, 1202, 1283, 1367, 1454, 1543, 1635, 1730, 1827, 1927, 2030, 2135, 2243, 2354, 2467, 2583, 2702, 2823, 2947, 3074

Offset: 0

Author

Paul Barry, Jan 19 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of number triangle A115284.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Programs

Mathematica

LinearRecurrence[{2,-1,1,-2,1},{1,3,7,14,23,35},50] (* Harvey P. Dale, Jul 27 2015 *)

Formula

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

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} [j<=k]*(4-C(1, k-j)-2*C(0, k-j))*[j<=n-2*k]*(4-C(1, n-2*k-j)-2*C(0, n-2*k-j)).