

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
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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(n1, k1)+F(k+1)*T(n1, k) where F(n)=A000045(n); Column k has g.f. x^k/Product(1F(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[n1, k1] + Fibonacci[k+1] F[n1, 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



