login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 21 04:58 EST 2014. Contains 252293 sequences.