A382479 Number of palindromic binary strings of length n having no 6-runs of 1's.

1, 2, 2, 4, 4, 8, 7, 15, 14, 30, 28, 60, 56, 119, 111, 236, 220, 468, 436, 928, 865, 1841, 1716, 3652, 3404, 7244, 6752, 14369, 13393, 28502, 26566, 56536, 52696, 112144, 104527, 222447, 207338, 441242, 411272, 875240, 815792, 1736111, 1618191, 3443720, 3209816, 6830904, 6366936

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

M. A. Nyblom, Counting Palindromic Binary Strings Without r-Runs of Ones, J. Int. Seq. 16 (2013) #13.8.7, P_6(n).

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,1,0,1,0,1,0,1).

Formula

G.f.: -(1+x+x^2)*(x^2-x+1)*(x^7+2*x+1)/(-1+x^2+x^4+x^6+x^8+x^10+x^12).

Mathematica

LinearRecurrence[{0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1}, {1, 2, 2, 4, 4, 8, 7, 15, 14, 30, 28, 60}, 50] (* Vincenzo Librandi, May 20 2025 *)

Prog

(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(-(1+x+x^2)*(x^2-x+1)*(x^7+2*x+1)/(-1+x^2+x^4+x^6+x^8+x^10+x^12))); // Vincenzo Librandi, May 20 2025

Crossrefs

Cf. A251707 (bisection), A251708 (bisection).

Cf. A123231 (2-runs), A001590 (3-runs), A382478 (4-runs), A251653 (5-runs).

Sequence in context: A100835 A347444 A120541 * A190172 A339820 A287293

Adjacent sequences: A382476 A382477 A382478 * A382480 A382481 A382482

Keyword

nonn,easy

Author

R. J. Mathar, Mar 28 2025

Status

approved