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 A173239 Triangle by columns, A000041 shifted down thrice, k>0 5
 1, 1, 2, 3, 1, 5, 1, 7, 2, 11, 3, 1, 15, 5, 1, 22, 7, 2, 30, 11, 3, 1, 42, 15, 5, 1, 56, 22, 7, 2, 77, 30, 11, 3, 1, 101, 42, 15, 5, 1, 135, 56, 22, 7, 2, 176, 77, 30, 11, 3, 1, 231, 101, 42, 15, 5, 1, 297, 135, 56, 22, 7, 2, 385, 176, 77, 30, 11, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums = A024787, the numbers of 3's in all partitions of n, where A024787 starts with offset 1: (0, 0, 1, 1, 2, 4, 6, 9, 15,...). Triangle A173239 row sums start with the first "1" of A024787. Let the triangle = M as an infinite lower triangular matrix. Then Lim_{n->inf} = A173241, the Euler transform of A051064 (the ruler function for 3). Let P(x) = polcoeff A000041 = (1 + x + 2x^2 + 3x^3 + 5x^4 + 7x^5 + ...), then P(x) = A(x) / A(x^3), where A(x) = polcoeff A173241: (1 + x + 2x^2 + 4x^3 + 6x^4 + ...) Refer to A173238 comments for three conjectures relating A000041 to the infinite set of generalized ruler function sequences. LINKS FORMULA Triangle by columns, A000041 shifted down thrice, k>0 MAPLE First few rows of the triangle = 1; 1; 2; 3, 1; 5, 1; 7, 2; 11, 3, 1; 15, 5, 1; 22, 7, 2; 30, 11, 3, 1; 42, 15, 5, 1; 56, 22, 7, 2; 77, 30, 11, 3, 1; 101, 42, 15, 5, 1; 135, 56, 22, 7, 2; 176, 77, 30, 11, 3, 1; 231, 101, 42, 15, 5, 1; 297, 135, 56, 22, 7, 2; 385, 176, 77, 30, 11, 3, 1; 490, 231, 101, 42, 15, 5, 1; 627, 297, 135, 56, 22, 7, 2; 792, 385, 176, 77, 30, 11, 3, 1; 1002, 490, 231, 101, 42, 15, 5, 1; 1255, 627, 297, 135, 56, 22, 7, 2; 1575, 792, 385, 176, 77, 30, 11, 3, 1; ... CROSSREFS Cf. A000041, A173238, A173241, A051064, A024787 Sequence in context: A251758 A250480 A166333 * A214055 A066909 A095195 Adjacent sequences:  A173236 A173237 A173238 * A173240 A173241 A173242 KEYWORD nonn,tabf AUTHOR Gary W. Adamson, Feb 13 2010 STATUS approved

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Last modified November 13 17:16 EST 2018. Contains 317149 sequences. (Running on oeis4.)