A117267 Difference row triangle of A117189.

1, 1, 2, 2, 3, 5, 4, 6, 9, 14, 7, 11, 17, 26, 40, 13, 20, 31, 48, 74, 114, 24, 37, 57, 88, 136, 210, 324, 44, 68, 105, 162, 250, 386, 596, 920, 81, 125, 193, 298, 460, 710, 1096, 1692, 2612, 149, 230, 355, 548, 846, 1306, 2016, 3112, 4804, 7416

Offset

1,3

Comments

Take difference rows of A117189 (binomial transform of the tribonacci sequence, A000073); and reorient to a flush left format.

Links

Table of n, a(n) for n=1..55.

Example

Taking difference rows of A117189, we get:
   1,  2,  5, 14, 40, 114, ...
   1,  3,  9, 26, 74, ...
   2,  6, 17, 48, ...
   4, 11, 31, ...
   7, 20, ...
  13, ...
Reorient into the triangle:
  1;
  1,  2;
  2,  3,  5;
  4,  6,  9, 14;
  7, 11, 17, 26, 40;
  ...

Prog

(PARI) lista(nn) = my(va = Vec(-(x-1)^2/(-1+4*x-4*x^2+2*x^3) + O(x^(nn))), v = vector(nn)); v[1] = va; for (n=2, nn, v[n] = vector(nn-n+1, k, v[n-1][k+1] - v[n-1][k]); ); my(list = List()); for (n=1, nn, my(i = n, j = 1); for (k=1, n, listput(list, v[i][j]); i--; j++; ); ); Vec(list); \\ Michel Marcus, Aug 10 2023

Crossrefs

Cf. A000073 (1st column), A117268 (difference rows), A117189 (right diagonal).

Sequence in context: A328666 A036716 A026399 * A086363 A174094 A360461

Adjacent sequences: A117264 A117265 A117266 * A117268 A117269 A117270

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 05 2006

Extensions

More terms from Michel Marcus, Aug 10 2023

Status

approved