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

0,1

Links

Table of n, a(n) for n=0..62.

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).

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001972, A078530.

Sequence in context: A060283 A255851 A334743 * A180017 A243827 A059530

Adjacent sequences: A078526 A078527 A078528 * A078530 A078531 A078532

Keyword

nonn,easy

Author

Michael Somos, Nov 25 2002

Status

approved