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A117267
Difference row triangle of A117189.
1
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.
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
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Mar 05 2006
EXTENSIONS
More terms from Michel Marcus, Aug 10 2023
STATUS
approved