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A036353
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Square pentagonal numbers.
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4
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OFFSET
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0,3
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COMMENTS
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lim(n -> Infinity, a(n)/a(n-1)) = (sqrt(2) + sqrt(3))^8 = 4801 + 1960*sqrt(6). - Ant King, Nov 06 2011
Pentgonal numbers (A000326) which are also centered octagonal numbers (A016754). - Colin Barker, Jan 11 2015
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LINKS
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Table of n, a(n) for n=0..9.
Eric Weisstein's World of Mathematics, Pentagonal Square Number
Index to sequences with linear recurrences with constant coefficients, signature (9603,-9603,1).
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FORMULA
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a(n) = 9602*a(n-1) - a(n-2) + 200; g.f.: x*(1+198*x+x^2)/((1-x)*(1-9602*x+x^2)). - Warut Roonguthai, Jan 05 2001
a(n+1) = 4801*a(n)+100+980*(24*a(n)^2+a(n))^0.5. - Richard Choulet, Sep 21 2007
From Ant King, Nov 06 2011: (Start)
a(n) = floor(1/96*(sqrt(2) + sqrt(3))^(8n-4)).
a(n) = 9603*a(n-1) - 9603*a(n-2) + a(n-3). (End)
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MATHEMATICA
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Table[Floor[1/96 ( Sqrt[2] + Sqrt[3] ) ^ ( 8*n - 4 ) ] , {n, 0, 9}] (* Ant King, Nov 06 2011 *)
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PROG
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(PARI) for(n=0, 10^9, g=(n*(3*n-1)/2); if(issquare(g), print(g)))
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CROSSREFS
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Cf. A000326, A001078, A001079, A001110, A046172, A046173, A248205.
Sequence in context: A156735 A227489 A113937 * A174769 A031687 A031597
Adjacent sequences: A036350 A036351 A036352 * A036354 A036355 A036356
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KEYWORD
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nonn,easy
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AUTHOR
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Jean-Francois Chariot (jeanfrancois.chariot(AT)afoc.alcatel.fr)
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EXTENSIONS
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More terms from Eric W. Weisstein
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STATUS
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approved
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