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A116445
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Triangle, row sums = Fibonacci numbers convolved with themselves.
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0
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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
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1,5
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COMMENTS
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First few rows of the array are:
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LINKS
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Table of n, a(n) for n=1..66.
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A001629, A104249.
Sequence in context: A027960 A218618 A131248 * A110291 A152027 A077308
Adjacent sequences: A116442 A116443 A116444 * A116446 A116447 A116448
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Feb 15 2006
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STATUS
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approved
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