

A081065


Numbers n such that n^2 = (1/3)*(n+floor(sqrt(3)*n*floor(sqrt(3)*n))).


2



2, 24, 330, 4592, 63954, 890760, 12406682, 172802784, 2406832290, 33522849272, 466913057514, 6503259955920, 90578726325362, 1261598908599144, 17571805994062650, 244743685008277952, 3408839784121828674, 47479013292697323480, 661297346313640700042
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OFFSET

1,1


COMMENTS

a(n)/2 gives indices of pentagonal numbers which are also triangular.
a(n) itself gives xvalues solving the Diophantine equation 2*x^2 + (x1)^2 = y^2.


LINKS

Table of n, a(n) for n=1..19.
Index entries for linear recurrences with constant coefficients, signature (15,15,1).


FORMULA

a(n) = 15*a(n1)  15*a(n2) + a(n3).
a(n) = 14*a(n1)  a(n2)  4. [Sture Sjöstedt, May 02 2011]
G.f.: 2*(13*x)/((1x)*(114*x+x^2)).  Bruno Berselli, Nov 11 2011


MATHEMATICA

LinearRecurrence[{15, 15, 1}, {2, 24, 330}, 20] (* Harvey P. Dale, Mar 14 2016 *)


PROG

(PARI) Vec(2*(13*x)/((1x)*(114*x+x^2)) + O(x^40)) \\ Michel Marcus, Nov 17 2014


CROSSREFS

Cf. A046090, A046174, A046175.
Sequence in context: A181174 A209290 A333715 * A043699 A220317 A220340
Adjacent sequences: A081062 A081063 A081064 * A081066 A081067 A081068


KEYWORD

nonn,easy


AUTHOR

Benoit Cloitre, Apr 15 2003


STATUS

approved



