A251653 -id:A251653 - cp's OEIS frontend

A382478 Number of palindromic binary strings of length n having no 4-runs of 1's.

1, 2, 2, 4, 3, 7, 6, 14, 12, 27, 23, 52, 44, 100, 85, 193, 164, 372, 316, 717, 609, 1382, 1174, 2664, 2263, 5135, 4362, 9898, 8408, 19079, 16207, 36776, 31240, 70888, 60217, 136641, 116072, 263384, 223736, 507689, 431265, 978602, 831290, 1886316, 1602363, 3635991, 3088654, 7008598, 5953572

Offset: 0

R. J. Mathar, Mar 28 2025

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_4(n).
Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,1,0,1).

Cf. A001630 (bisection), A001631 (bisection).

Cf. A123231 (2-runs), A001590 (3-runs), A251653 (5-runs), A382479 (6-runs).

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(-(x^2+1)*(x^5+2*x+1) / (-1+x^2+x^4+x^6+x^8))); // Vincenzo Librandi, May 19 2025

LinearRecurrence[{0,1,0,1,0,1,0,1},{1,2,2,4,3,7,6,14},50] (* Vincenzo Librandi, May 19 2025 *)

G.f.: -(x^2+1)*(x^5+2*x+1)/(-1+x^2+x^4+x^6+x^8).

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

Original entry on oeis.org

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

R. J. Mathar, Mar 28 2025

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).

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

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

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

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 *)

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).

cp's OEIS Frontend

A382478 Number of palindromic binary strings of length n having no 4-runs of 1's.

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