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A157103 Triangle by columns, generalized Fibonacci sequences. 3
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 3, 1, 1, 5, 12, 10, 4, 1, 1, 8, 29, 33, 17, 5, 1, 1, 13, 70, 109, 72, 26, 6, 1, 1, 21, 169, 360, 305, 135, 37, 7, 1, 1, 34, 408, 1189, 1292, 701, 228, 50, 8, 1, 1, 55, 985, 3927, 5473, 3640, 1405, 357, 65, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

Michelle Rudolph-Lilith, On the Product Representation of Number Sequences, with Application to the Fibonacci Family, arXiv preprint arXiv:1508.07894, 2015. See Table 3.

FORMULA

Triangle by columns, k-th column is a generalized Fibonacci sequence of the form S(n) = k*S(n-1) + S(n-2).

EXAMPLE

First few rows of the triangle =

1;

1, 1;

1, 1, 1;

1, 2, 2, 1;

1, 3, 5, 3, 1;

1, 5, 12, 10, 4, 1;

1, 8, 29, 33, 17, 5, 1;

1, 13, 70, 109, 72, 26, 6, 1;

1, 21, 169, 360, 305, 135, 37, 7, 1;

1, 34, 408, 1189, 1292, 701, 228, 50, 8, 1;

1, 55, 985, 3927, 5473, 3640, 1405, 357, 65, 9, 1;

1, 89, 2378, 12970, 23184, 18901, 8658, 2549, 528, 82, 10, 1;

1, 144, 5741, 42837, 98209, 98145, 53353, 18200, 4289, 747, 101, 11, 1;

...

Example: Column 3 = (1, 3, 10, 33, 109, 360,...) = A006190

MATHEMATICA

T[_, 0] = 1;

T[n_, n_] = 1;

T[n_, k_] /; 0 <= k <= n := k T[n-1, k] + T[n-2, k];

T[_, _] = 0;

Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Aug 07 2018 *)

CROSSREFS

Cf. A000045, A000129, A006190, A001076, A052918, A005668, A054413, A041025, A099371

Sequence in context: A132044 A034327 A034254 * A135966 A292741 A060351

Adjacent sequences:  A157100 A157101 A157102 * A157104 A157105 A157106

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Feb 22 2009

STATUS

approved

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)