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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: A325331 A333108 A266935 * A051693 A266470 A371745 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 July 20 17:15 EDT 2024. Contains 374459 sequences. (Running on oeis4.)