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!)
A048915 9-gonal pentagonal numbers. 2
1, 651, 180868051, 95317119801, 26472137730696901, 13950766352135999751, 3874504486629442861646551, 2041856512426320950146560501, 567078683619272811125915867157001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Contribution from Ant King, Dec 20 2011: (Start)

lim(n->Infinity, a(2n+1)/a(2n))=1/2*(277727+60605*sqrt(21)).

lim(n->Infinity, a(2n)/a(2n-1))=1/2*(527+115*sqrt(21)).

(End)

LINKS

Table of n, a(n) for n=1..9.

Eric Weisstein's World of Mathematics, Nonagonal Pentagonal Number.

Index entries for sequences related to linear recurrences with constant coefficients, signature (1,146361602,-146361602,-1,1).

FORMULA

Contribution from Ant King, Dec 20 2011: (Start)

a(n) = 146361602*a(n-2)-a(n-4)+35719200.

a(n) = a(n-1)+146361602*a(n-2)-146361602*a(n-3)-a(n-4)+a(n-5).

a(n) = 1/336*((25+4*sqrt(21))*(5-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(4n-4)+ (25-4*sqrt(21))*(5+sqrt(21)*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(4n-4)-82).

a(n) = floor(1/336*(25+4*sqrt(21))*(5-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(4n-4)).

G.f.: x*(1+650*x+34505798*x^2+1210450*x^3+2301*x^4) / ((1-x)*(1-12098*x+x^2)*(1+12098*x+x^2)).

(End)

MATHEMATICA

LinearRecurrence[{1, 146361602, -146361602, -1, 1}, {1, 651, 180868051, 95317119801, 26472137730696901}, 9] (* Ant King, Dec 20 2011 *)

CROSSREFS

Cf. A048913, A048914.

Sequence in context: A151736 A010087 A110850 * A002232 A127029 A127030

Adjacent sequences:  A048912 A048913 A048914 * A048916 A048917 A048918

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

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 17 18:04 EST 2014. Contains 252034 sequences.