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A133284 Indices of the 12-gonal numbers which are also centered 12-gonal number or numbers X such that 30*X^2-24*X+3 is a square. 0
1, 13, 277, 6073, 133321, 2926981, 64260253, 1410798577, 30973308433, 680001986941, 14929070404261, 327759546906793, 7195780961545177, 157979421607087093, 3468351494394370861, 76145753455069071841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..16.

Index entries for linear recurrences with constant coefficients, signature (23,-23,1)

FORMULA

a(n+2)=22*a(n+1)-a(n)-8 ; a(n+1)=11*a(n)-4+2*(30*a(n)^2-24*a(n)+3)^0.5

a(n)=(2/5)+(3/10)*[11+2*sqrt(30)]^n+(1/20)*[11+2*sqrt(30)]^n*sqrt(30)+(3/10)*[11-2 *sqrt(30)]^n-(1/20)*sqrt(30)*[11-2*sqrt(30)]^n, with n>=0 [From Paolo P. Lava, Aug 06 2008]

G.f.: x(1-10x+x^2)/((1-x)(1-22x+x^2)). [From R. J. Mathar, Oct 30 2008]

MATHEMATICA

Rest[CoefficientList[Series[x (1-10x+x^2)/((1-x)(1-22x+x^2)), {x, 0, 20}], x]] (* or *) LinearRecurrence[{23, -23, 1}, {1, 13, 277}, 20] (* Harvey P. Dale, Nov 07 2019 *)

CROSSREFS

Sequence in context: A295096 A295550 A320336 * A012570 A256044 A160294

Adjacent sequences:  A133281 A133282 A133283 * A133285 A133286 A133287

KEYWORD

nonn

AUTHOR

Richard Choulet, Oct 16 2007

EXTENSIONS

More terms from Paolo P. Lava, Aug 06 2008

STATUS

approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)