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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

Table of n, a(n) for n=0..45.

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: A218700 A325331 A266935 * A051693 A266470 A209700

Adjacent sequences:  A175009 A175010 A175011 * A175013 A175014 A175015

KEYWORD

nonn,tabl,more

AUTHOR

Gary W. Adamson, Apr 03 2010

STATUS

approved

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Last modified November 11 18:50 EST 2019. Contains 329031 sequences. (Running on oeis4.)