A078529 Exponent sequence for a bilinear recursive sequence.

3, 1, 0, 0, 0, 0, 0, 1, 2, 3, 4, 6, 9, 10, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, 51, 55, 60, 66, 72, 78, 84, 91, 98, 105, 112, 120, 129, 136, 144, 153, 162, 171, 180, 190, 200, 210, 220, 231, 243, 253, 264, 276, 288, 300, 312, 325, 338, 351, 364, 378, 393, 406, 420

Offset: 0

Author

Michael Somos, Nov 25 2002

Keywords

• nonn
• easy

Examples

			3 + x + x^7 + 2*x^8 + 3*x^9 + 4*x^10 + 6*x^11 + 9*x^12 + 10*x^13 + ...
		

Links

• Index entries for two-way infinite sequences
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,0,1,-2,1).

Crossrefs

Cf. A001972, A078530.

Programs

Mathematica

LinearRecurrence[{2,-1,0,0,0,0,0,0,0,0,0,1,-2,1},{3,1,0,0,0,0,0,1,2,3,4,6,9,10},70] (* Harvey P. Dale, May 27 2017 *)

PARI

{a(n) = (n%12==0) + (n-4)^2\8}

Formula

G.f.: (3 - 5*x + x^2 + x^3 + x^7 + x^11 - 2*x^12 + 3*x^13) / ((1 - x)^2 * (1 - x^12)).

a(8-n) - a(n) = -1 if n == 0 (mod 12), +1 if n == 8 (mod 12), 0 otherwise.