A081670 a(n) = 3^n-1+C(2n,n).

1, 4, 14, 46, 150, 494, 1652, 5618, 19430, 68302, 243804, 882578, 3235596, 11994922, 44899568, 169466426, 644127110, 2462746382, 9462555788, 36507525266, 141333313220, 548718227642, 2135480023328, 8327573906426, 32530033219580

Offset

0,2

Comments

Binomial transform of A081669.

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = A000984(n) + 2*A003462(n).

E.g.f.: exp(3*x)-exp(x)+exp(2*x)*BesselI_0(2*x).

Conjecture: n*(3*n^2-17*n+26)*a(n) +2*(-12*n^3+71*n^2-131*n+60)*a(n-1) +(57*n^3-347*n^2+710*n-480)*a(n-2) -6*(2*n-5)*(3*n^2-11*n+12)*a(n-3) = 0. - R. J. Mathar, Nov 12 2012

Example

a(6) = 1652; 3^6 - 1 + binomial(12,6) = 728 + 924 = 1652.

Maple

A081670:=n->3^n-1+binomial(2*n, n); seq(A081670(k), k=0..50); # Wesley Ivan Hurt, Nov 04 2013

Mathematica

Table[3^n - 1 + Binomial[2 n, n], {n, 0, 50}] (* Wesley Ivan Hurt, Nov 04 2013 *)

Crossrefs

Cf. A000984, A003462, A081669.

Sequence in context: A027649 A330796 A049221 * A297016 A258255 A124805

Adjacent sequences: A081667 A081668 A081669 * A081671 A081672 A081673

Keyword

easy,nonn,changed

Author

Paul Barry, Mar 28 2003

Status

approved