A188645 - OEIS

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A188645

Array of ((k^n)+(k^(-n)))/2 where k=((x^2+1)^(1/2)+x)^2 for integers x>=1

1, 3, 1, 17, 9, 1, 99, 161, 19, 1, 577, 2889, 721, 33, 1, 3363, 51841, 27379, 2177, 51, 1, 19601, 930249, 1039681, 143649, 5201, 73, 1, 114243, 16692641, 39480499, 9478657, 530451, 10657, 99, 1 (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; 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 A188644`
	LINKS	`Table of n, a(n) for n=0..35.`
	FORMULA	`a(n)=(A188647(n-1)+A188647(n))/2`
	EXAMPLE	`1, 3, 17, 99, 577, 3363, 19601, 114243, ...` `1, 9, 161, 2889, 51841, 930249, 16692641, ...` `1, 19, 721, 27379, 1039681, 39480499, ...` `1, 33, 2177, 143649, 9478657, 625447713, ...` `1, 51, 5201, 530451, 54100801, ...` `1, 73, 10657, 1555849, 227143297, ...` `1, 99, 19601, 3880899, 768398401, ...` `1, 129, 33281, 8586369, 2215249921, ...` `1, 163, 53137, 17322499, 5647081537, ...` `1, 201, 80801, 32481801, 13057603201, ...` `1, 243, 118097, 57394899, 27893802817, ...` `1, 289, 167041, 96549409, 55805391361, ...` `1, 339, 229841, 155831859, 105653770561, ...` `1, 393, 308897, 242792649, 190834713217, ...` `1, 451, 406801, 366934051, 330974107201, ...` `...`
	CROSSREFS	`Row 1 is A001541, row 2 is A023039, row 3 is A078986, row 4 is A099370, row 5 is A099397, row 6 is A174747, row 8 is A176368, (row 1)2 is A003499, (row 2)2 is A087215.` `Column 2 is A058331, (column 2)2 is A005899.` `A188644 (f(x, y) as above with y=-1).` `Sequence in context: A096611 A176666 A162313 A060281 A151918 A089974` `Adjacent sequences: A188642 A188643 A188644 * A188646 A188647 A188648`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Charles L. Hohn, Apr 06 2011`
	STATUS	`approved`

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Last modified May 22 05:06 EDT 2013. Contains 225511 sequences.