A138749 a(n) = 2*a(n-1) - 5*a(n-2).

-1, -7, -9, 17, 79, 73, -249, -863, -481, 3353, 9111, 1457, -42641, -92567, 28071, 518977, 897599, -799687, -6087369, -8176303, 14084239, 69049993, 67678791, -209892383, -758178721, -466895527, 2857102551, 8048682737, 1811852719, -36619708247

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Index entries for linear recurrences with constant coefficients, signature (2,-5).

Formula

a(n) = 2*a(n-1) - 5*a(n-2), n>3.

a(n) = left term in [1,-2; 2,1]^n * [1,1].

O.g.f.: -x*(1+5*x)/(1-2*x+5*x^2). a(n)=-A045873(n)-5*A045873(n-1). - R. J. Mathar, Apr 03 2008

a(n) = (1/2)*(1+i)*((1+2*i)^n-i*(1-2*i)^n), where i=sqrt(-1). - Bruno Berselli, Jul 06 2011

Example

a(5) = 79 = 2*a(4) - 5*a(3) = 2*17 - 5*(-9).
a(5) = 79 = left term in [1,-2, 2,1]^5.

Prog

(PARI) a(n)={local(v=Vec((1+2*I*x)^n)); sum(k=1, #v, real(v[k])-imag(v[k])); } /* cf. A116483 */ /* Joerg Arndt, Jul 06 2011 */

Crossrefs

Sequence in context: A255830 A256613 A116484 * A320700 A053803 A320323

Adjacent sequences: A138746 A138747 A138748 * A138750 A138751 A138752

Keyword

sign,easy

Author

Gary W. Adamson, Mar 28 2008

Status

approved