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 A188644 Array of ((k^n)+(k^(-n)))/2 where k=((x^2-1)^(1/2)+x)^2 for integers x>=1 9
 1, 1, 1, 1, 7, 1, 1, 97, 17, 1, 1, 1351, 577, 31, 1, 1, 18817, 19601, 1921, 49, 1, 1, 262087, 665857, 119071, 4801, 71, 1, 1, 3650401, 22619537, 7380481, 470449, 10081, 97, 1, 1, 50843527, 768398401 (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; and constant k=f(x, y); then for all integers x>=1 and y=[+-]1, k may be irrational, but ((k^n)+(k^(-n)))/2 always produces integer sequences; y=-1 results shown here; y=1 results are A188645 LINKS FORMULA a(n)=(A188646(n-1)+A188646(n))/2 EXAMPLE 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 7, 97, 1351, 18817, 262087, 3650401, ... 1, 17, 577, 19601, 665857, 22619537, ... 1, 31, 1921, 119071, 7380481, 457470751, ... 1, 49, 4801, 470449, 46099201, ... 1, 71, 10081, 1431431, 203253121, ... 1, 97, 18817, 3650401, 708158977, ... 1, 127, 32257, 8193151, 2081028097, ... 1, 161, 51841, 16692641, 5374978561, ... 1, 199, 79201, 31521799, 12545596801, ... 1, 241, 116161, 55989361, 26986755841, ... 1, 287, 164737, 94558751, 54276558337, ... 1, 337, 227137, 153090001, 103182433537, ... 1, 391, 305761, 239104711, 186979578241, ... 1, 449, 403201, 362074049, 325142092801, ... ... CROSSREFS Row 2 is A011943, row 3 is A056771, row 8 is A175633, (row 2)*2 is A067902, (row 9)*2 is A089775. Column 2 is A056220 (difference in starting term), (column 2)*2 is A060626. A188645 (f(x, y) as above with y=1). Sequence in context: A015118 A174691 A156692 * A111830 A212943 A174588 Adjacent sequences:  A188641 A188642 A188643 * A188645 A188646 A188647 KEYWORD nonn,tabl AUTHOR Charles L. Hohn, Apr 06 2011 STATUS approved

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