

A156070


Triangle read by rows based on the Fibonacci sequence A000045: t(n,m) = 1 + Fibonacci[n]  Fibonacci[m]  Fibonacci[n  m].


4



1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 3, 2, 1, 1, 3, 5, 5, 5, 3, 1, 1, 5, 8, 9, 9, 8, 5, 1, 1, 8, 13, 15, 16, 15, 13, 8, 1, 1, 13, 21, 25, 27, 27, 25, 21, 13, 1, 1, 21, 34, 41, 45, 46, 45, 41, 34, 21, 1
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OFFSET

0,13


COMMENTS

Row sums are {1, 2, 2, 4, 6, 12, 23, 46, 90, 174, 330,...} (see A188538).
More generally, we can define for a sequence with a(n)=0 : add one;
t(n,m)=1+a(n)a(m)a(nm)
or a(0)=1: add two:
t(n,m)=2+a(n)a(m)a(nm).


LINKS

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


FORMULA

t(n,m)=1 + Fibonacci[n]  Fibonacci[m]  Fibonacci[n  m].


EXAMPLE

{1},
{1, 1},
{1, 0, 1},
{1, 1, 1, 1},
{1, 1, 2, 1, 1},
{1, 2, 3, 3, 2, 1},
{1, 3, 5, 5, 5, 3, 1},
{1, 5, 8, 9, 9, 8, 5, 1},
{1, 8, 13, 15, 16, 15, 13, 8, 1},
{1, 13, 21, 25, 27, 27, 25, 21, 13, 1},
{1, 21, 34, 41, 45, 46, 45, 41, 34, 21, 1}


MATHEMATICA

t[n_, m_] = 1 + Fibonacci[n]  Fibonacci[m]  Fibonacci[n  m];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]


CROSSREFS

Cf. A000045, A188538.
Sequence in context: A125769 A272084 A003023 * A323670 A114731 A035389
Adjacent sequences: A156067 A156068 A156069 * A156071 A156072 A156073


KEYWORD

nonn,tabl


AUTHOR

Roger L. Bagula, Feb 03 2009


EXTENSIONS

Edited by N. J. A. Sloane, Apr 03 2011


STATUS

approved



