A083862 Main diagonal of array A083857.

0, 1, 3, 10, 39, 171, 819, 4229, 23247, 135088, 824163, 5255361, 34876647, 240130801, 1710323667, 12572548582, 95183606559, 740843916471, 5918533467075, 48463830575837, 406239439253175, 3481899731310196

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = (((3 + sqrt(4*n + 1))/2)^n - ((3 - sqrt(4*n + 1))/2)^n)/sqrt(4*n + 1).

Maple

T := proc(n, k) local v; option remember; if 0 <= n and k = 0 then v := 0; end if; if 0 <= n and k = 1 then v := 1; end if; if 0 <= n and 2 <= k then v := 3*T(n, k - 1) + (n - 2)*T(n, k - 2); end if; v; end proc;
seq(T(n, n), n = 0 .. 40); # Petros Hadjicostas, Dec 25 2019

Crossrefs

Cf. A083857, A083859, A083863.

Sequence in context: A245378 A350915 A221585 * A205543 A137590 A352174

Adjacent sequences: A083859 A083860 A083861 * A083863 A083864 A083865

Keyword

easy,nonn

Author

Paul Barry, May 06 2003

Status

approved