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A133274 Numbers which are both 12-gonal and centered 12-gonal numbers. 0
1, 793, 382537, 184382353, 88871911921, 42836077163881, 20646900321079033, 9951763118682930337, 4796729176304851343713, 2312013511215819664739641, 1114385715676848773553163561, 537131602942729893032960097073 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We write G12(r)=5*r^2-4*r and CG12(p)=6*p^2-6*p+1. A number has both properties iff there exist r and p such that 2*(5*r-2)^2=15*(2*p-1)^2+3. The Diophantine equation (2*X)^2=30*Y^2+6 gives 2 new sequences. We obtain also 2 new sequences with the indices given by r and p respectively.

LINKS

Table of n, a(n) for n=1..12.

Index entries for linear recurrences with constant coefficients, signature (483,-483,1).

FORMULA

a(n+2)=482*a(n+1)-a(n)+312 ; a(n+1)=241*a(n)+156+44*(30*a(n)^2+39*a(n)+12)^0.5 ;

G.f.: (z+310*z^2+z^3)/((1-z)*(1-482*z+z^2)).

a(n)=-(13/20)+(33/40)*{[241+44*sqrt(30)]^n+[241-44*sqrt(30)]^n}-(3/20)*sqrt(30)*{[241-44*sqrt(30)]^n-[241+44*sqrt(30)]^n }, with n>=0 [From Paolo P. Lava, Nov 25 2008]

CROSSREFS

Sequence in context: A213471 A075667 A136543 * A261657 A086393 A108251

Adjacent sequences:  A133271 A133272 A133273 * A133275 A133276 A133277

KEYWORD

nonn,easy

AUTHOR

Richard Choulet, Oct 16 2007

STATUS

approved

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Last modified August 18 14:09 EDT 2017. Contains 290720 sequences.