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Search: id:A076218
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| A076218 |
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Numbers n such that 2*n^2 - 3*n + 1 is a square. |
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+0
3
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| 0, 1, 5, 145, 4901, 166465, 5654885, 192099601, 6525731525, 221682772225, 7530688524101, 255821727047185, 8690408031080165, 295218051329678401, 10028723337177985445, 340681375412721826705, 11573138040695364122501
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OFFSET
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1,3
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COMMENT
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Lim n -> Inf. a(n)/a(n-1) = 33.970562748477140585620264690516 = 17 + 12*Sqrt(2).
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FORMULA
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Formula: ( (3+(17+12*sqrt(2))^(n-1)) + (3+(17-12*sqrt(2))^(n-1)) )/8 for n>=1; Recurrence: a(n) = 35*(a(n-1)-a(n-2))+a(n-3) with a(1) = 1, a(2) = 5, a(3) = 145; Generating function = (x-30*x^2+5*x^3)/(1-35*x+35*x^2-x^3). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 04 2002
Product of adjacent odd subscripted Pell series numbers (A000129). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 07 2003
Sqrt(2) - 1 = .414213562...= 2/5 + 2/145 + 2/4901 + 2/166465...= Sum (2 through infinity) 2/a(n). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 07 2003
For n>0, one more than square of adjacent even subscripted Pell series numbers (A000129). - Charlie Marion (charliemath(AT)optonline.net), Mar 09 2005
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CROSSREFS
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Sequence in context: A037049 A134503 A081322 this_sequence A075186 A113560 A094364
Adjacent sequences: A076215 A076216 A076217 this_sequence A076219 A076220 A076221
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KEYWORD
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nonn
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AUTHOR
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Gregory V. Richardson (omomom(AT)hotmail.com), Nov 03 2002
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