A388548 Triangle read by rows: T(n,k) is the number of length n binary palindromic words which are not all zero in which 1's occur in blocks of at least k.

1, 1, 1, 3, 1, 1, 3, 2, 1, 1, 7, 3, 2, 1, 1, 7, 4, 2, 2, 1, 1, 15, 6, 4, 2, 2, 1, 1, 15, 8, 4, 3, 2, 2, 1, 1, 31, 11, 7, 4, 3, 2, 2, 1, 1, 31, 15, 7, 5, 3, 3, 2, 2, 1, 1, 63, 20, 12, 7, 5, 3, 3, 2, 2, 1, 1, 63, 27, 12, 8, 5, 4, 3, 3, 2, 2, 1, 1, 127, 36, 20, 11, 8, 5, 4, 3, 3, 2, 2, 1, 1

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Formula

T(n,k) = A388200(n,k) - 1.

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

Example

Triangle begins:
   1;
   1,  1;
   3,  1,  1;
   3,  2,  1, 1;
   7,  3,  2, 1, 1;
   7,  4,  2, 2, 1, 1;
  15,  6,  4, 2, 2, 1, 1;
  15,  8,  4, 3, 2, 2, 1, 1;
  31, 11,  7, 4, 3, 2, 2, 1, 1;
  31, 15,  7, 5, 3, 3, 2, 2, 1, 1;
  63, 20, 12, 7, 5, 3, 3, 2, 2, 1, 1;
  63, 27, 12, 8, 5, 4, 3, 3, 2, 2, 1, 1;
  ...

Crossrefs

Columns 1..3 are A052551(n-1), A023434(n-1), A131524, A386709.

Cf. A388200, A388547.

Sequence in context: A106749 A225224 A140216 * A176514 A238559 A077196

Adjacent sequences: A388545 A388546 A388547 * A388549 A388550 A388551

Keyword

nonn,tabl

Author

Andrew Howroyd, Sep 18 2025

Status

approved