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 A174067 Triangle, row sums = A000041 starting (1, 2, 3, 5, 7,...); derived from finite differences of p(x) = A(x)*A(x^2) = B(x)*B(x^3) = C(x)*C(x^4) = ... 5
 1, 1, 1, 2, 0, 1, 3, 1, 0, 1, 4, 1, 1, 0, 1, 5, 2, 2, 1, 0, 1, 7, 2, 3, 1, 1, 0, 1, 9, 4, 3, 3, 1, 1, 0, 1, 12, 5, 5, 3, 3, 0, 1, 0, 1, 15, 8, 6, 5, 3, 2, 1, 1, 0, 1, 19, 10, 9, 6, 5, 2, 2, 1, 1, 0, 1, 25, 13, 12, 10, 5, 5, 2, 2, 1, 1, 0, 1, 31, 17, 16, 12, 9, 5, 4, 2, 2, 1, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums = A000041 starting with offset 1: (1, 2, 3, 5, 7, 11,...). LINKS FORMULA Given an array of rows satisfying p(x) = A(x)*A(x^2) = row 1 = A174065; row = 2 A174068 satisfying p(x) = B(x)*B(x^3);, row 3 satisfies p(x) = C(x)*C(x^4),...and so on; take finite differences from the top, becoming rows of triangle A174067 EXAMPLE First few rows of the array = 1, 1, 1, 2, 3, 4,. 5,..7,..9,..12,..15,..19,... = A174065 1, 1, 2, 2, 4, 5,. 7,..9,.13,..17,..23,..29,... = A174068 1, 1, 2, 3, 4, 6,. 9,.12,.16,..22,..29,..38,... satisfies p(x) = C(x)*C(x^4) 1, 1, 2, 3, 5, 6,.10,.13,.19,..25,..34,..44,... analogous for k=5 1, 1, 2, 3, 5, 7,.10,.14,.20,..28,..37,..49,..................k=6 1, 1, 2, 3, 5, 7,.11,.14,.21,..28,..39,..51,..................k=7 1, 1, 2, 3, 5, 7,.11,.15,.21,..29,..40,..53,..................k=8 1, 1, 2, 3, 5, 7,.11,.15,.22,..29,..41,..54,..................k=9 1, 1, 2, 3, 5, 7,.11,.15,.22,..30,..41,..55,..................k=10 ... Finally, take finite differences from the top, deleting the first 1, to obtain triangle A174067 1; 1, 1; 2, 0, 1; 3, 1, 0, 1; 4, 1, 1, 0, 1; 5, 2, 2, 1, 0, 1; 7, 2, 3, 1, 1, 0, 1; 9, 4, 3, 3, 1, 1, 0, 1; 12, 5, 5, 3, 3, 0, 1, 0, 1; 15, 8, 6, 5, 3, 2, 1, 1, 0, 1; 19, 10, 9, 6, 5, 2, 2, 1, 1, 0, 1; 25, 13, 12, 10, 5, 5, 2, 2, 1, 1, 0, 1; 31, 17, 16, 12, 9, 5, 4, 2, 2, 1, 1, 0, 1; 38, 24, 20, 18, 11, 8, 5, 4, 2, 2, 1, 1, 0, 1; ... CROSSREFS Sequence in context: A272472 A100260 A165317 * A124943 A169803 A099557 Adjacent sequences:  A174064 A174065 A174066 * A174068 A174069 A174070 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Mar 06 2010 STATUS approved

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Last modified October 16 08:03 EDT 2018. Contains 316259 sequences. (Running on oeis4.)