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A175012 Triangle generated from the g.f of A000712 (i.e., 1/(1-x^m)^2) interleaved with zeros. 1
1, 2, 2, 3, 2, 4, 4, 2, 4, 9, 5, 2, 4, 10, 14, 6, 2, 4, 10, 19, 23, 7, 2, 4, 10, 20, 34, 32, 8, 2, 4, 10, 20, 39, 55, 46, 9, 2, 4, 10, 20, 40, 66, 88, 60, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Row sums of the triangle = A000712.
LINKS
FORMULA
Given 1/(1-x^m)^2 = S(x) = (1 + 2x + 3x^2 + ...), let a = S(x), b = S(x^2) (i.e., S(x) interleaved with one zero); S(x^3) = S(x) interleaved with two zeros = c, etc.; then row 1 = a, row 2 = a*b, row 3 = a*b*c, ...
Take finite differences of the array from the top down, becoming rows of the triangle.
EXAMPLE
First few rows of the array =
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
1, 2, 5, 8, 14, 20, 30, 40, 55, 70, ...
1, 2, 5, 10, 18, 30, 49, 74, 110, 158, ...
1, 2, 5, 10, 20, 34, 59, 94, 149, 224, ...
1, 2, 5, 10, 20, 36, 63, 104, 169, 264, ...
1, 2, 5, 10, 20, 36, 65, 108, 179, 284, ...
...
First few rows of the triangle =
1;
2;
2, 3;
2, 4, 4;
2, 4, 9, 5;
2, 4, 10, 14, 6;
2, 4, 10, 19, 23, 7;
2, 4, 10, 20, 34, 32, 8;
2, 4, 10, 20, 39, 55, 46, 9;
2, 4, 10, 20, 40, 66, 88, 60, 10;
...
CROSSREFS
Cf. A000712.
Sequence in context: A325331 A333108 A266935 * A051693 A266470 A371745
KEYWORD
nonn,tabl,more
AUTHOR
Gary W. Adamson, Apr 03 2010
STATUS
approved

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Last modified July 20 17:15 EDT 2024. Contains 374459 sequences. (Running on oeis4.)