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A105037 a(0) = 0, a(1) = 4, a(2) = 6, a(3) = 98, for n>3 a(n) = 22*a(n-2) - a(n-4) + 10. 2
0, 4, 6, 98, 142, 2162, 3128, 47476, 68684, 1042320, 1507930, 22883574, 33105786, 502396318, 726819372, 11029835432, 15956920408, 242153983196, 350325429614, 5316357794890, 7691202531110, 116717717504394, 168856130254816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

It appears this sequence gives all nonnegative m such that 120*m^2 + 120*m + 1 is a square.

LINKS

Table of n, a(n) for n=0..22.

FORMULA

G.f.:-2*x*(2*x^2+x+2)/((x-1)*(x^4-22*x^2+1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

a(n)=-1/2-1/5*(11 + 2*sqrt(30))^(1/4*(-1)^n)*(-1)^n*(11 + 2*sqrt(30))^(1/2*n)*(11 + 2 *sqrt(30))^(-1/4)*sqrt(30) + 5/4*(11 + 2*sqrt(30))^(1/4*(-1)^n)*(11 + 2*sqrt(30))^(1/2 *n)*(11 + 2*sqrt(30))^(-1/4) + 5/24*(11 + 2*sqrt(30))^(1/4*(-1)^n)*(11 + 2*sqrt(30))^(1/2*n)*(11 + 2*sqrt(30))^(-1/4)*sqrt(30)-5/24*(11-2*sqrt(30))^(-1/4)*sqrt(30)*(11-2 *sqrt(30))^(1/4*(-1)^n)*(11-2*sqrt(30))^(1/2*n) + 5/4*(11-2*sqrt(30))^(-1/4)*(11-2 *sqrt(30))^(1/4*(-1)^n)*(11-2*sqrt(30))^(1/2*n)-(11 + 2*sqrt(30))^(1/4*(-1)^n)*( -1)^n*(11 + 2*sqrt(30))^(1/2*n)*(11 + 2*sqrt(30))^(-1/4) + 1/5*(-1)^n*(11-2 *sqrt(30))^(-1/4)*sqrt(30)*(11-2*sqrt(30))^(1/4*(-1)^n)*(11-2*sqrt(30))^(1/2*n) -(-1)^n*(11-2*sqrt(30))^(-1/4)*(11-2*sqrt(30))^(1/4*(-1)^n)*(11-2*sqrt(30))^(1/2*n), with n>=0 [From Paolo P. Lava, Aug 28 2009]

CROSSREFS

Cf. A077421.

Sequence in context: A087934 A052684 A213128 * A139730 A013023 A012909

Adjacent sequences:  A105034 A105035 A105036 * A105038 A105039 A105040

KEYWORD

nonn

AUTHOR

Gerald McGarvey, Apr 03 2005

STATUS

approved

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Last modified January 23 03:08 EST 2019. Contains 319370 sequences. (Running on oeis4.)