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 A188646 Array 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 9
 1, 1, 1, 1, 13, 1, 1, 181, 33, 1, 1, 2521, 1121, 61, 1, 1, 35113, 38081, 3781, 97, 1, 1, 489061, 1293633, 234361, 9505, 141, 1, 1, 6811741, 43945441, 14526601, 931393, 20021, 193, 1, 1, 94875313 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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 A188647 LINKS FORMULA a(n)=A188644(n)*2-a(n-1) EXAMPLE 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 13, 181, 2521, 35113, 489061, 6811741, ... 1, 33, 1121, 38081, 1293633, 43945441, ... 1, 61, 3781, 234361, 14526601, 900414901, ... 1, 97, 9505, 931393, 91267009, ... 1, 141, 20021, 2842841, 403663401, ... 1, 193, 37441, 7263361, 1409054593, ... 1, 253, 64261, 16322041, 4145734153, ... 1, 321, 103361, 33281921, 10716675201, ... 1, 397, 158005, 62885593, 25028308009, ... 1, 481, 231841, 111746881, 53861764801, ... 1, 573, 328901, 188788601, 108364328073, ... 1, 673, 453601, 305726401, ... 1, 781, 610741, 477598681, ... 1, 897, 805505, 723342593, ... ... CROSSREFS Row 1 is A000012, row 2 is A001570, row 3 is A077420. Column 2 is A082109. A188647 (f(x, y) as above with y=1). Sequence in context: A156539 A172300 A022176 * A174791 A015132 A066036 Adjacent sequences:  A188643 A188644 A188645 * A188647 A188648 A188649 KEYWORD nonn,tabl AUTHOR Charles L. Hohn, Apr 06 2011 STATUS approved

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Last modified August 16 00:25 EDT 2018. Contains 313782 sequences. (Running on oeis4.)