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

Author

R. J. Mathar, Mar 28 2025

Keywords

• nonn
• easy

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).

Crossrefs

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

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

Programs

Magma

m:=50; R:=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

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 *)

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).