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A105046 a(0)=0, a(1)=1, a(2)=8, a(3)=145, a(4)=1298*a(1)-648-a(3), a(5)=1298*a(2)-648-a(2), a(6)=1298*a(3)-a(0)-648-a(1), for n>6 a(n) = 1298*a(n-3) - a(n-6) - 648. 0
0, 1, 8, 145, 505, 9728, 187561, 654841, 12626288, 243453385, 849982465, 16388911448, 316002305521, 1103276584081, 21272794432568, 410170749112225, 1432052156154025, 27612070784561168, 532401316345361881, 1858802595411339721, 35840446605565962848 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

It appears this sequence gives all nonnegative m such that 13*m^2 - 13*m + 1 is a square and that a(n+1) = A104240(n) + 1. (A104240 is nonnegative n such that 13*n^2 + 13*n + 1 is a square.)

LINKS

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1298, -1298, 0, -1, 1).

FORMULA

G.f.: x (1+7x+137x^2-938x^3+137x^4+7x^5+x^6) / ((1-x) (1-11x+x^2) (1+11x+120x^2+11x^3+x^4). [From R. J. Mathar, Sep 09 2008]

MATHEMATICA

CoefficientList[Series[x (1+7x+137x^2-938x^3+137x^4+7x^5+x^6)/((1-x) (1-11x+x^2) (1+11x+120x^2+11x^3+x^4)), {x, 0, 30}], x] (* or *) Join[{0}, LinearRecurrence[{1, 0, 1298, -1298, 0, -1, 1}, {1, 8, 145, 505, 9728, 187561, 654841}, 30]] (* Harvey P. Dale, Jun 12 2012 *)

CROSSREFS

Cf. A104240.

Sequence in context: A231851 A071305 A172150 * A123812 A064331 A230938

Adjacent sequences:  A105043 A105044 A105045 * A105047 A105048 A105049

KEYWORD

nonn

AUTHOR

Gerald McGarvey, Apr 03 2005

EXTENSIONS

More terms from Harvey P. Dale, Jun 12 2012

STATUS

approved

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Last modified September 18 17:45 EDT 2019. Contains 327178 sequences. (Running on oeis4.)