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 A188647 Array read by anti-diagonals of a(n)=a(n-1)*k-((k-1)/(k^n)) where a(0)=1 and k=((x^2+1)^(1/2)+x)^2 for integers x>=1 16
 1, 5, 1, 29, 17, 1, 169, 305, 37, 1, 985, 5473, 1405, 65, 1, 5741, 98209, 53353, 4289, 101, 1, 33461, 1762289, 2026009, 283009, 10301, 145, 1, 195025, 31622993, 76934989, 18674305, 1050601, 21169, 197 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture by C Hohn: Given function f(x, y)=((x^2+y)^(1/2)+x)^2; constant k=f(x, y); and initial term a(0)=1; then for all integers x>=1 and y=[+-]1, k may be irrational, but sequence a(n)=a(n-1)*k-((k-1)/(k^n)) always produces integer sequences; y=1 results shown here; y=-1 results are A188646 LINKS FORMULA a(n)=A188645(n)*2-a(n-1) EXAMPLE 1, 5, 29, 169, 985, 5741, 33461, 195025, ... 1, 17, 305, 5473, 98209, 1762289, ... 1, 37, 1405, 53353, 2026009, 76934989, ... 1, 65, 4289, 283009, 18674305, ... 1, 101, 10301, 1050601, 107151001, ... 1, 145, 21169, 3090529, 451196065, ... 1, 197, 39005, 7722793, 1529074009, ... 1, 257, 66305, 17106433, 4413393409, ... 1, 325, 105949, 34539049, 11259624025, ... 1, 401, 161201, 64802401, 26050404001, ... 1, 485, 235709, 114554089, 55673051545, ... 1, 577, 333505, 192765313, 111418017409, ... 1, 677, 459005, 311204713, ... 1, 785, 617009, 484968289, ... 1, 901, 812701, 733055401, ... ... CROSSREFS Row 1 is A001653, row 2 is A007805, row 3 is A097315, row 4 is A078988, row 5 is A097727, row 6 is A097730, row 7 is A097733, row 8 is A097736, row 9 is A097739, row 10 is A097742, row 11 is A097767, row 12 is A097770, row 13 is A097773. Column 2 is A053755. Cf. A188646 (f(x, y) as above with y=-1). Sequence in context: A125906 A146414 A146374 * A214882 A144890 A144891 Adjacent sequences:  A188644 A188645 A188646 * A188648 A188649 A188650 KEYWORD nonn,tabl AUTHOR Charles L. Hohn, Apr 06 2011 STATUS approved

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