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

Author

Gary W. Adamson, Mar 05 2006

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
  ...
		

Crossrefs

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

Programs

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

Extensions

More terms from Michel Marcus, Aug 10 2023