A386709 Number of length n binary palindromic words which are not all zero in which 1's occur in blocks of at least 4.

0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 7, 8, 11, 13, 17, 21, 26, 33, 40, 51, 62, 78, 96, 119, 148, 182, 227, 279, 347, 428, 530, 656, 810, 1004, 1239, 1535, 1896, 2346, 2901, 3586, 4437, 5483, 6784, 8385, 10371, 12823, 15855, 19608, 24241, 29980, 37065, 45836, 56674, 70078, 86655

Offset

1,6

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

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

Formula

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

Example

The a(10) = 5 words are: 1111111111, 1111001111, 0111111110, 001111110, 0001111000.
The a(11) = 7 words are: 11111111111, 11111011111, 11110001111, 01111111110, 01111011110, 0011111110, 00011111000.

Crossrefs

Column 4 of A388548.

Cf. A209231.

Sequence in context: A304329 A111901 A316202 * A326671 A134727 A152305

Adjacent sequences: A386706 A386707 A386708 * A386710 A386711 A386712

Keyword

nonn,easy

Author

Andrew Howroyd, Sep 18 2025

Status

approved