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A111669 Triangle read by rows, based on a simple Fibonacci recursion rule. 3
1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 11, 7, 1, 1, 5, 26, 32, 12, 1, 1, 6, 57, 122, 92, 20, 1, 1, 7, 120, 423, 582, 252, 33, 1, 1, 8, 247, 1389, 3333, 2598, 681, 54, 1, 1, 9, 502, 4414, 18054, 24117, 11451, 1815, 88, 1, 1, 10, 1013, 13744, 94684, 210990, 172980, 49566 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Subdiagonal is A000071(n+3). Row sums of inverse are 0^n.

Row sums are given by A135934 - Emanuele Munarini, Dec 05 2017

LINKS

Table of n, a(n) for n=0..62.

FORMULA

Number triangle T(n, k)=T(n-1, k-1)+F(k+1)*T(n-1, k) where F(n)=A000045(n); Column k has g.f. x^k/Product(1-F(j+1)x, j, 0, k).

EXAMPLE

Triangle begins

1....1....2....3....5....8...13....F(k+1)

1

1....1

1....2....1

1....3....4....1

1....4...11....7....1

1....5...26...32...12....1

1....6...57..122...92...20....1

For example, T(6,3)=122=26+3*32=T(5,2)+F(4)*T(5,3)

MATHEMATICA

(* To generate the triangle *)

Grid[RecurrenceTable[{F[n, k] == F[n-1, k-1] + Fibonacci[k+1] F[n-1, k], F[0, k] == KroneckerDelta[k]}, F, {n, 0, 10}, {k, 0, 10}]] (* Emanuele Munarini, Dec 05 2017 *)

CROSSREFS

Cf. A111577, A111578, A111579, A008277, A039755, A135934.

Sequence in context: A063841 A256161 A137596 * A336573 A124834 A271465

Adjacent sequences: A111666 A111667 A111668 * A111670 A111671 A111672

KEYWORD

easy,nonn,tabl

AUTHOR

Gary W. Adamson, Aug 14 2005

EXTENSIONS

Edited by Paul Barry, Nov 14 2005

STATUS

approved

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Last modified December 4 02:16 EST 2022. Contains 358544 sequences. (Running on oeis4.)