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A036411
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9-gonal square numbers.
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4
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1, 9, 1089, 8281, 978121, 7436529, 878351769, 6677994961, 788758910641, 5996832038649, 708304623404049, 5385148492712041, 636056763057925561, 4835857349623374369, 571178264921393749929, 4342594514813297471521
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OFFSET
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1,2
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COMMENTS
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From Ant King, Nov 17 2011: (Start)
lim( n -> Infinity, a(2n+1)/a(2n)) = 1/625 * (36913 + 9864 * sqrt(14))
lim( n -> Infinity, a(2n)/a(2n-1)) = 1/625 * (2417 + 624 * sqrt(14))
(End)
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Nonagonal Square Number.
Index to sequences with linear recurrences with constant coefficients, signature (1,898,-898,-1,1)
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FORMULA
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O.g.f f(z)=1+9*z+...= ((1+8*z+182*z^2+8*z^3+z^4)/((1-z)*(1-898*z^2+z^4))). With the first values, for n >+0 : a(n+5)=a(n+4)+898*a(n+3)-898*a(n+2)-a(n+1)+a(n). On every bisection modulo 2 : a(n+2)=30*a(n+1)-a(n)+200. On every bisection modulo 2 : a(n+1)=449*a(n)+100+60*sqrt(56*a(n)^2+25*a(n)). a(n)=(-25/112)+ ((11/28)+(11/112)*sqrt(14))*(15+4*sqrt(14))^n+ ((11/28)-(11/112)*sqrt(14))*(15-4*sqrt(14))^n+ ((7/32)-(1/16)*sqrt(14))*(-15+4*sqrt(14))^n+((7/32)+(1/16)*sqrt(14))*(-15-4*sqrt(14))^n [From Richard Choulet, May 08 2009]
a(n) = 898 * a(n-2) - a(n-4) + 200. - Ant King, Nov 17 2011
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MAPLE
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a(0):=1:a(1):=9:a(2):=1089:a(3):=8281: a(4):=978121:for n from 0 to 20 do a(n+5):=a(n+4)+898*a(n+3)-898*a(n+2)-a(n+1)+a(n):od:seq(a(n), n=0..20); [From Richard Choulet, May 08 2009]
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MATHEMATICA
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LinearRecurrence[ {1, 898, - 898, - 1, 1 }, { 1, 9, 1089, 8281, 978121 }, 16] (* Ant King, Nov 17 2011 *)
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PROG
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(MAGMA) I:=[1, 9, 1089, 8281]; [n le 4 select I[n] else 898*Self(n-2)-Self(n-4)+200: n in [1..20]]; // Vincenzo Librandi, Nov 18 2011
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CROSSREFS
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Cf. A048919, A048911, A001106.
Sequence in context: A174636 A054344 A048912 * A075412 A174253 A084149
Adjacent sequences: A036408 A036409 A036410 * A036412 A036413 A036414
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KEYWORD
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easy,nonn
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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
More terms from Richard Choulet, May 08 2009
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STATUS
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approved
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