A259713 a(n) = 3*2^n - 2*(-1)^n.

1, 8, 10, 26, 46, 98, 190, 386, 766, 1538, 3070, 6146, 12286, 24578, 49150, 98306, 196606, 393218, 786430, 1572866, 3145726, 6291458, 12582910, 25165826, 50331646, 100663298, 201326590, 402653186, 805306366, 1610612738, 3221225470, 6442450946, 12884901886

Offset: 0

Author

Paul Curtz, Jul 03 2015

Keywords

• nonn
• easy

Comments

Inverse binomial transform of 3^n, with 3 (second term) excluded.

a(n) mod 9 gives A010689.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Crossrefs

Cf. A000244, A005010, A007283, A010689, A096045, A140788, A182460, A201630.

Programs

Magma

[3*2^n-2*(-1)^n: n in [0..40]]; // Vincenzo Librandi, Jul 04 2015

Mathematica

Table[3 2^n - 2 (-1)^n, {n, 0, 50}] (* Vincenzo Librandi, Jul 04 2015 *)
LinearRecurrence[{1,2},{1,8},40] (* Harvey P. Dale, Aug 19 2020 *)

PARI

Vec(-(7*x+1)/((x+1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Jul 03 2015

Formula

a(n) = a(n-1) + 2*a(n-2) for n>1, a(0)=1, a(1)=8.

a(n) = 2*a(n-1) - 6*(-1)^n for n>0, a(0)=1.

a(4n+2) = 10*A182460(n); a(2n) = A096045(n), a(2n+1) = A140788(n).

a(n) = 3*A014551(n+1) - A201630(n).

a(n+2) - a(n) = a(n) + a(n+1) = A005010(n).

G.f.: -(7*x+1) / ((x+1)*(2*x-1)). - Colin Barker, Jul 03 2015

Extensions

Typo in data fixed by Colin Barker, Jul 03 2015