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A133271 Indices of 7-gonal numbers which are also centered 7-gonal numbers. 0
1, 8, 92, 1093, 13021, 155156, 1848848, 22031017, 262523353, 3128249216, 37276467236, 444189357613, 5292995824117, 63071760531788, 751568130557336, 8955745806156241, 106717381543317553, 1271652832713654392 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers X such that 140*X^2-84*X-7 is a square.

LINKS

Table of n, a(n) for n=1..18.

Index entries for linear recurrences with constant coefficients, signature (13, -13, 1).

FORMULA

a(n+2)=12*a(n+1)-a(n)-3 ; a(n+1)=6*a(n)-1.5+0.5*(140*a(n)^2-84*a(n)-7)^0.5

G.f.: -x*(1-5*x+x^2)/(-1+x)/(1-12*x+x^2). - R. J. Mathar, Nov 14 2007

a(n)=3/10+(7/20)*[6-sqrt(35)]^(n-1)+(1/20)*sqrt(35)*[6+sqrt(35)]^(n-1)+(7/20)*[6+sqrt(35)]^(n-1)-(1/20) *[6-sqrt(35)]^(n-1)*sqrt(35), with n>=1 - Paolo P. Lava, Jul 08 2008

a(1)=1, a(2)=8, a(3)=92, a(n)=13*a(n-1)-13*a(n-2)+a(n-3). - Harvey P. Dale, Mar 24 2013

MATHEMATICA

LinearRecurrence[{13, -13, 1}, {1, 8, 92}, 30] (* Harvey P. Dale, Mar 24 2013 *)

CROSSREFS

Cf. A128919.

Sequence in context: A322650 A221765 A292842 * A180903 A266427 A239644

Adjacent sequences:  A133268 A133269 A133270 * A133272 A133273 A133274

KEYWORD

nonn

AUTHOR

Richard Choulet, Oct 16 2007

EXTENSIONS

More terms from Paolo P. Lava, Jul 08 2008

STATUS

approved

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)