A115217 Diagonal sums of "correlation triangle" for 2^n.

1, 2, 6, 13, 30, 62, 133, 270, 558, 1125, 2286, 4590, 9253, 18542, 37230, 74533, 149358, 298862, 598309, 1196910, 2394990, 4790565, 9583470, 19168110, 38340901, 76684142, 153377646, 306759973, 613538670, 1227086702, 2454210853

Offset

0,2

Comments

Diagonal sums of number triangle A003983.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-3,-2,-2,4).

Formula

a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, [j<=k]*2^(k-j)[j<=n-2k]2^(n-2k-j)}}.

G.f.: 1/((1-2x)(1-2x^2)(1-x^3)); a(n)=2a(n-1)+2a(n-2)-3a(n-3)-2a(n-4)-2a(n-5)+4a(n-6); - Paul Barry, Jan 18 2006

Mathematica

LinearRecurrence[{2, 2, -3, -2, -2, 4}, {1, 2, 6, 13, 30, 62}, 40] (* Harvey P. Dale, Oct 18 2021 *)

Crossrefs

Sequence in context: A288979 A289048 A297388 * A094687 A369584 A336875

Adjacent sequences: A115214 A115215 A115216 * A115218 A115219 A115220

Keyword

easy,nonn

Author

Paul Barry, Jan 16 2006

Status

approved