

A116445


Triangle, row sums = Fibonacci numbers convolved with themselves.


0



1, 1, 1, 1, 3, 1, 1, 3, 5, 1, 1, 3, 8, 7, 1, 1, 3, 8, 16, 9, 1, 1, 3, 8, 20, 27, 11, 1, 1, 3, 8, 20, 43, 41, 13, 1, 1, 3, 8, 20, 48, 81, 58, 15, 1, 1, 3, 8, 20, 48, 106, 138, 78, 17, 1, 1, 3, 8, 20, 48, 112, 213, 218, 101, 19, 1
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OFFSET

1,5


COMMENTS

First few rows of the array are:


LINKS

Table of n, a(n) for n=1..66.


FORMULA

Create an array by rows: (binomial transforms of 1,0,0,0,...; 1,2,0,0,0...; 1,2,3,0,0,0...; etc.). Antidiagonals of the array become rows of the triangle.


EXAMPLE

1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
1, 3, 5, 7, 9, 11, 13, 15, 17,...
1, 3, 8, 16, 27, 41, 58, 78, 101,...
1, 3, 8, 20, 43, 81, 138, 218,...
1, 3, 8, 20, 48, 106, 213,...
1, 3, 8, 20, 48, 112, 249,...
...
Rows converge to A001792, binomial transform of (1,2,3...); and the first few rows of the triangle are:
1
1, 1;
1, 3, 1;
1, 3, 5, 1;
1, 3, 8, 7, 1;
1, 3, 8, 16, 9, 1;
1, 3, 8, 20, 27, 22, 1;
...
Row sums are Fibonacci numbers convolved with themselves (A001629: 1, 2, 5, 10, 20, 38, 71, 130, 235, 420...).
a(4), a(5), a(6) = 1, 3, 1 = antidiagonals of the array becoming row three of the triangle.


CROSSREFS

Cf. A001629, A104249.
Sequence in context: A027960 A218618 A131248 * A110291 A152027 A077308
Adjacent sequences: A116442 A116443 A116444 * A116446 A116447 A116448


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Feb 15 2006


STATUS

approved



