A388200 - OEIS

A388200

Array read by antidiagonals: T(n,k) is the number of length n binary palindromic words in which 1's occur in blocks of at least k, n >= 0, k >= 1.

1, 1, 2, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 2, 4, 1, 1, 1, 2, 3, 8, 1, 1, 1, 1, 2, 4, 8, 1, 1, 1, 1, 2, 3, 5, 16, 1, 1, 1, 1, 1, 2, 3, 7, 16, 1, 1, 1, 1, 1, 2, 3, 5, 9, 32, 1, 1, 1, 1, 1, 1, 2, 3, 5, 12, 32, 1, 1, 1, 1, 1, 1, 2, 3, 4, 8, 16, 64, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 8, 21, 64

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)

R. K. Guy, Anyone for Twopins?, in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15. [Annotated scanned copy, with permission]

FORMULA

G.f. of column k: (1 + x + x^k)/(1 - x^2 - x^(k+1)).

EXAMPLE

Array begins:

================================================

n\k| 1 2 3 4 5 6 7 8 9 10 11 12 ...

-----+------------------------------------------

0 | 1 1 1 1 1 1 1 1 1 1 1 1 ...

1 | 2 1 1 1 1 1 1 1 1 1 1 1 ...

2 | 2 2 1 1 1 1 1 1 1 1 1 1 ...

3 | 4 2 2 1 1 1 1 1 1 1 1 1 ...

4 | 4 3 2 2 1 1 1 1 1 1 1 1 ...

5 | 8 4 3 2 2 1 1 1 1 1 1 1 ...

6 | 8 5 3 3 2 2 1 1 1 1 1 1 ...

7 | 16 7 5 3 3 2 2 1 1 1 1 1 ...

8 | 16 9 5 4 3 3 2 2 1 1 1 1 ...

9 | 32 12 8 5 4 3 3 2 2 1 1 1 ...

10 | 32 16 8 6 4 4 3 3 2 2 1 1 ...

11 | 64 21 13 8 6 4 4 3 3 2 2 1 ...

...

PROG

(PARI) T(n, k) = polcoef((1 + x + x^k)/(1 - x^2 - x^(k+1)) + O(x*x^n), n)

CROSSREFS

Columns 1..5 are A060546, A134816(n+2), A103609(n+3), A005686(n+2), A108104(n+1).

Cf. A388146 (not necessarily symmetric).

Sequence in context: A377365 A326371 A226304 * A101022 A241153 A389761

Adjacent sequences: A388197 A388198 A388199 * A388201 A388202 A388203

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Sep 15 2025

STATUS

approved