A172285 a(n) = (5*2^n - 5*(-1)^n - 3*n*(-1)^n) / 9.

0, 2, 1, 6, 7, 20, 33, 74, 139, 288, 565, 1142, 2271, 4556, 9097, 18210, 36403, 72824, 145629, 291278, 582535, 1165092, 2330161, 4660346, 9320667, 18641360, 37282693, 74565414, 149130799, 298261628, 596523225, 1193046482, 2386092931, 4772185896

Offset: 0

Author

Paul Curtz, Jan 30 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,2).

Crossrefs

Cf. A000079, A001045, A053088, A141291, A164044.

Programs

Magma

[(5*2^n - 5*(-1)^n - 3*n*(-1)^n) / 9: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

Maple

A172295 := proc(n) (5*2^n - 5*(-1)^n - 3*n*(-1)^n) / 9 ; end proc: seq(A172295(n), n=0..100) ; # R. J. Mathar, Feb 02 2010

Mathematica

Table[(5*2^n - 5*(-1)^n - 3*n*(-1)^n)/9, {n, 0, 40}] (* Wesley Ivan Hurt, Aug 27 2015 *)

PARI

first(m)=vector(m,i,i--;(5*2^i -5*(-1)^i - 3*i*(-1)^i ) / 9) \\ Anders Hellström, Aug 27 2015

Formula

a(n) = 3*a(n-2) + 2*a(n-3), n>2.

a(n+1) = 2*a(n) + (-1)^n * (2+n).

a(n) = A053088(n-1) + A001045(n), n>0.

a(n) = A000079(n) - A053088(n).

a(2n) = A141291(n). a(2n+1) = 2*A164044(n).

G.f.: x*(2+x)/( (1-2*x)*(1+x)^2 ).

Extensions

Definition replaced by explicit formula; g.f. added - R. J. Mathar, Feb 02 2010