A115285 - OEIS

%I #11 Jan 22 2025 05:23:03

%S 1,3,7,14,23,35,50,67,87,110,135,163,194,227,263,302,343,387,434,483,

%T 535,590,647,707,770,835,903,974,1047,1123,1202,1283,1367,1454,1543,

%U 1635,1730,1827,1927,2030,2135,2243,2354,2467,2583,2702,2823,2947,3074

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

%C Diagonal sums of number triangle A115284.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

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

%F 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)).

%t LinearRecurrence[{2,-1,1,-2,1},{1,3,7,14,23,35},50] (* _Harvey P. Dale_, Jul 27 2015 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jan 19 2006