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
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).
Programs
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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.