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A048915 9-gonal pentagonal numbers. 3
1, 651, 180868051, 95317119801, 26472137730696901, 13950766352135999751, 3874504486629442861646551, 2041856512426320950146560501, 567078683619272811125915867157001, 298849390212849227278846377616002051, 82998544594567922836927983404875025948251 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Colin Barker, Table of n, a(n) for n = 1..246

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

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

FORMULA

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 *)

PROG

(PARI) Vec(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)) + O(x^20)) \\ Colin Barker, Jun 22 2015

CROSSREFS

Cf. A048913, A048914.

Sequence in context: A010087 A110850 A257715 * A257827 A261552 A002232

Adjacent sequences:  A048912 A048913 A048914 * A048916 A048917 A048918

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified December 3 18:47 EST 2016. Contains 278745 sequences.