A062113 a(0)=1; a(1)=2; a(n) = a(n-1) + a(n-2)*(3 - (-1)^n)/2.

1, 2, 3, 7, 10, 24, 34, 82, 116, 280, 396, 956, 1352, 3264, 4616, 11144, 15760, 38048, 53808, 129904, 183712, 443520, 627232, 1514272, 2141504, 5170048, 7311552, 17651648, 24963200, 60266496, 85229696, 205762688, 290992384, 702517760

Offset: 0

Author

Olivier Gérard, Jun 05 2001

Keywords

• easy
• nonn

Comments

A bistable recurrence.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-2).

Crossrefs

Cf. A007068, A062112.

Programs

Haskell

a062113 n = a062113_list !! n
a062113_list = 1 : 2 : zipWith (+)
   (tail a062113_list) (zipWith (*) a000034_list a062113_list)
-- Reinhard Zumkeller, Jan 21 2012

Magma

I:=[1,2,3,7]; [n le 4 select I[n] else 4*Self(n-2) - 2*Self(n-4): n in [1..40]]; // G. C. Greubel, Oct 16 2018

Mathematica

LinearRecurrence[{0,4,0,-2}, {1,2,3,7}, 40] (* G. C. Greubel, Oct 16 2018 *)

PARI

{ for (n=0, 200, if (n>1, a=a1 + a2*(3 - (-1)^n)/2; a2=a1; a1=a, if (n==0, a=a2=1, a=a1=2)); write("b062113.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 01 2009

PARI

x='x+O('x^40); Vec((1+2*x-x^2-x^3)/(1-4*x^2+2*x^4)) \\ G. C. Greubel, Oct 16 2018

Formula

a(n) = a(n-1) + a(n-2) * A000034(n). - Reinhard Zumkeller, Jan 21 2012

From Colin Barker, Apr 20 2012: (Start)

a(n) = 4*a(n-2) - 2*a(n-4).

G.f.: (1+2*x-x^2-x^3)/(1-4*x^2+2*x^4). (End)