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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 10:07 EDT 2014. Contains 246995 sequences.