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

0,2

Comments

Diagonal sums of number triangle A115284.

Links

Table of n, a(n) for n=0..48.

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

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)).

Mathematica

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

Crossrefs

Sequence in context: A377122 A213077 A294400 * A004232 A140462 A227841

Adjacent sequences: A115282 A115283 A115284 * A115286 A115287 A115288

Keyword

easy,nonn

Author

Paul Barry, Jan 19 2006

Status

approved