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A115266 Row sums of correlation triangle for floor((n+3)/3). 1

%I

%S 1,2,4,8,13,20,31,44,61,84,111,144,186,234,291,360,438,528,634,752,

%T 886,1040,1210,1400,1615,1850,2110,2400,2715,3060,3441,3852,4299,4788,

%U 5313,5880,6496,7154,7861,8624,9436,10304,11236,12224,13276,14400,15588

%N Row sums of correlation triangle for floor((n+3)/3).

%C Row sums of number triangle A115265.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-3,0,3,0,0,-2,1).

%F G.f.: (1+x+x^2)^2/((1-x^3)^4*(1-x^2)); a(n)=sum{k=0..n, sum{j=0..n, [j<=k]*floor((k-j+3)/3)*[j<=n-k]*floor((n-k-j+3)/3)}}.

%t T[n_, k_] := Sum[Boole[j <= k] * Floor[(k - j + 3)/3] * Boole[j <= n - k] * Floor[(n - k - j + 3)/3], {j, 0, n}]; a[n_] := Sum[T[n, k], {k, 0, n}]; Table[a[n], {n, 0, 46}] (* _Jean-Fran├žois Alcover_, Jul 15 2017 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jan 18 2006

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)