A057174 a(n+3)=a(n)+a(n+1)-a(n+2), starting with 1,2,3.

1, 2, 3, 0, 5, -2, 7, -4, 9, -6, 11, -8, 13, -10, 15, -12, 17, -14, 19, -16, 21, -18, 23, -20, 25, -22, 27, -24, 29, -26, 31, -28, 33, -30, 35, -32, 37, -34, 39, -36, 41, -38, 43, -40, 45, -42, 47, -44, 49, -46, 51, -48, 53, -50, 55, -52, 57, -54, 59, -56, 61, -58, 63, -60, 65, -62, 67, -64, 69, -66, 71, -68, 73, -70, 75, -72

Offset: 0

Author

Gregory V. Richardson, Oct 17 2000

Keywords

• easy
• sign

Examples

			a(4)=0 because 1+2-3=0
		

Links

• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• Index entries for linear recurrences with constant coefficients, signature (-1,1,1).

Programs

Mathematica

LinearRecurrence[{-1,1,1},{1,2,3},80] (* Harvey P. Dale, Jul 15 2023 *)

Formula

O.g.f.: (1+3x+4x^2)/((1-x)(1+x)^2). a(n)=2+(n-1)*(-1)^n. [From R. J. Mathar, Aug 22 2008]

Extensions

More terms from James Sellers, Oct 18 2000