A168258 Triangle read by rows, A101688 * A000012 as infinite lower triangular matrices.

1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 3, 3, 3, 2, 1, 3, 3, 3, 3, 2, 1, 4, 4, 4, 4, 3, 2, 1, 4, 4, 4, 4, 4, 3, 2, 1, 5, 5, 5, 5, 5, 4, 3, 2, 1, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 6, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1

Offset

1,4

Comments

Row sums = A001318, general pentagonal numbers: (1, 2, 5, 12, 15, 22, ...).

Eigensequence of the triangle = A168259: (1, 2, 6, 14, 38, 96, 254, 656, ...).

The operation A101688 * A000012 transforms rows of A101688 into sequence terms by taking partial sums from the right of A101688 rows. For example, row 3 of A101688 (0, 0, 1, 1) becomes (2, 2, 2, 1). - Gary W. Adamson, Nov 15 2022

Links

Table of n, a(n) for n=1..78.

Formula

Triangle read by rows, A101688 * A000012 as infinite lower triangular matrices.

a(n) = min(A004736, A204164); a(n) = min(j, floor((t+2)/2)), where j=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Apr 18 2013

Example

First few rows of the triangle:
  1;
  1, 1;
  2, 2, 1;
  2, 2, 2, 1;
  3, 3, 3, 2, 1;
  3, 3, 3, 3, 2, 1;
  4, 4, 4, 4, 3, 2, 1;
  4, 4, 4, 4, 4, 3, 2, 1;
  5, 5, 5, 5, 5, 4, 3, 2, 1;
  5, 5, 5, 5, 5, 5, 4, 3, 2, 1;
  6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1;
  6, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1;
  7, 7, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1;
  7, 7, 7, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1;
  8, 8, 8, 8, 8, 8, 8, 8, 7, 6, 5, 4, 3, 2, 1;
  ...

Prog

(PARI) T(n, k) = if(binomial(k, n-k)>0, 1, 0); \\ A101688
lista(nn) = my(ma=matrix(nn+1, nn, n, k, T(n-1, k-1)), mb=matrix(nn, nn, n, k, n>=k)); my(m=ma*mb, list=List()); for (n=1, nn, listput(list, vector(n, k, m[n, k]))); Vec(list); \\ Michel Marcus, Nov 16 2022

Crossrefs

Cf. A001318, A101688, A000012, A168259, A004736, A204164.

Sequence in context: A107260 A338236 A279346 * A116204 A291592 A159905

Adjacent sequences: A168255 A168256 A168257 * A168259 A168260 A168261

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 21 2009

Extensions

Name corrected by Gary W. Adamson, Nov 15 2022

Status

approved