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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
OFFSET
1,1
COMMENTS
a(n)/2 gives indices of pentagonal numbers which are also triangular.
a(n) itself gives x-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2.
FORMULA
a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3).
a(n) = 14*a(n-1) - a(n-2) - 4. [Sture Sjöstedt, May 02 2011]
G.f.: 2*(1-3*x)/((1-x)*(1-14*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*(1-3*x)/((1-x)*(1-14*x+x^2)) + O(x^40)) \\ Michel Marcus, Nov 17 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Apr 15 2003
STATUS
approved