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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

Table of n, a(n) for n=0..37.

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 September 22 20:30 EDT 2018. Contains 315270 sequences. (Running on oeis4.)