A188644 - OEIS

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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

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	`Table of n, a(n) for n=0..38.`
	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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Last modified May 23 09:48 EDT 2013. Contains 225586 sequences.