This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 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 entries for 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 A266602 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 | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.