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).
From Paul Barry, Jan 18 2006: (Start)
G.f.: 1/((1-2*x)*(1-2*x^2)*(1-x^3)).
a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3) - 2*a(n-4) - 2*a(n-5) + 4*a(n-6). (End)
E.g.f.: (exp(x)*(7 + 48*exp(x)) + 2*exp(-x/2)*cos(sqrt(3)*x/2) - 36*cosh(sqrt(2)*x) - 30*sqrt(2)*sinh(sqrt(2)*x))/21. - Stefano Spezia, Aug 28 2025
MATHEMATICA
LinearRecurrence[{2, 2, -3, -2, -2, 4}, {1, 2, 6, 13, 30, 62}, 40] (* Harvey P. Dale, Oct 18 2021 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 16 2006
STATUS
approved
