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 A117267 Difference row triangle of A117189. 1

%I #16 Aug 10 2023 15:36:03

%S 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,

%T 136,210,324,44,68,105,162,250,386,596,920,81,125,193,298,460,710,

%U 1096,1692,2612,149,230,355,548,846,1306,2016,3112,4804,7416

%N Difference row triangle of A117189.

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

%e Taking difference rows of A117189, we get:

%e 1, 2, 5, 14, 40, 114, ...

%e 1, 3, 9, 26, 74, ...

%e 2, 6, 17, 48, ...

%e 4, 11, 31, ...

%e 7, 20, ...

%e 13, ...

%e Reorient into the triangle:

%e 1;

%e 1, 2;

%e 2, 3, 5;

%e 4, 6, 9, 14;

%e 7, 11, 17, 26, 40;

%e ...

%o (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

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

%K nonn,tabl

%O 1,3

%A _Gary W. Adamson_, Mar 05 2006

%E More terms from _Michel Marcus_, Aug 10 2023

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Last modified March 5 03:04 EST 2024. Contains 370537 sequences. (Running on oeis4.)