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A036411 9-gonal square numbers. 4
1, 9, 1089, 8281, 978121, 7436529, 878351769, 6677994961, 788758910641, 5996832038649, 708304623404049, 5385148492712041, 636056763057925561, 4835857349623374369, 571178264921393749929, 4342594514813297471521 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)

LINKS

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)

FORMULA

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

MAPLE

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]

MATHEMATICA

LinearRecurrence[ {1, 898, - 898, - 1, 1 }, { 1, 9, 1089, 8281, 978121 }, 16] (* Ant King, Nov 17 2011 *)

PROG

(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

CROSSREFS

Cf. A048919, A048911, A001106.

Sequence in context: A174636 A054344 A048912 * A075412 A174253 A084149

Adjacent sequences:  A036408 A036409 A036410 * A036412 A036413 A036414

KEYWORD

easy,nonn

AUTHOR

Jean-Francois Chariot (jeanfrancois.chariot(AT)afoc.alcatel.fr)

EXTENSIONS

More terms from Eric W. Weisstein

More terms from Richard Choulet, May 08 2009

STATUS

approved

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Last modified April 23 19:18 EDT 2014. Contains 240946 sequences.