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A048913 Indices of 9-gonal numbers which are also pentagonal. 3
1, 14, 7189, 165026, 86968201, 1996480214, 1052141284189, 24153417459626, 12728805169146001, 292208042430070814, 153993083884187031589, 3535132873165579243826, 1863008316102089539013401, 42768037207349135261731814, 22538674454209995358797089389 (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*(527+115*sqrt(21))

lim(n->Infinity, a(2n)/a(2n-1))=1/2*(23+5*sqrt(21))

(End)

LINKS

Colin Barker, Table of n, a(n) for n = 1..490

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

Index entries for linear recurrences with constant coefficients, signature (1,12098,-12098,-1,1).

FORMULA

From Ant King, Dec 20 2011: (Start)

a(n) = 12098*a(n-2)-a(n-4)-4320.

a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5).

a(n) = 1/84*((2+sqrt(21))*(sqrt(21)-3*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2)-(2-sqrt(21))*( sqrt(21)+3*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(2n-2)+30).

a(n) = ceiling(1/84*(2+sqrt(21))*(sqrt(21)-3*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2)).

G.f.: x*(1+13*x-4923*x^2+563*x^3+26*x^4) / ((1-x)*(1-110*x+x^2)*(1+110*x+x^2)).

(End)

MATHEMATICA

LinearRecurrence[{1, 12098, -12098, -1, 1}, {1, 14, 7189, 165026, 86968201}, 13] (* Ant King, Dec 20 2011 *)

PROG

(PARI) Vec(-x*(26*x^4+563*x^3-4923*x^2+13*x+1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^20)) \\ Colin Barker, Jun 22 2015

CROSSREFS

Cf. A048914, A048915.

Sequence in context: A030531 A206357 A147686 * A246623 A208194 A104376

Adjacent sequences:  A048910 A048911 A048912 * A048914 A048915 A048916

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified March 26 12:27 EDT 2019. Contains 321497 sequences. (Running on oeis4.)