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A073352 Positive integers making n^2(n-1)(2n-1)^2(7n-1)/36 a square. 2
1, 4, 55, 868, 13825, 220324, 3511351, 55961284, 891869185, 14213945668, 226531261495, 3610286238244, 57538048550401, 916998490568164, 14614437800540215, 232914006318075268, 3712009663288664065 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

G.f.: (1-13x+4x^2)/((1-x)(1-16x+x^2)). a(n)=16a(n-1)-a(n-2)-8. (Corrected by Paolo P. Lava, Jun 19 2008)

a(n)=4/7+(3/14)*[8-3*sqrt(7)]^n+(3/14)*[8+3*sqrt(7)]^n, with n>=0 - Paolo P. Lava, Jun 19 2008

EXAMPLE

1 + 4*x + 55*x^2 + 868*x^3 + 13825*x^4 + 220324*x^5 + 3511351*x^6 + ...

PROG

(PARI) {a(n) = if( n<0, a(-n), if( n<1, 1, 16*a(n-1) - a(n-2) - 8))}

(PARI) {a(n) = (4 + 3 * real((8 + 3 * quadgen(28))^n)) / 7}

CROSSREFS

Cf. A007750.

Sequence in context: A204107 A285366 A202163 * A258793 A195634 A206384

Adjacent sequences:  A073349 A073350 A073351 * A073353 A073354 A073355

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 27 2002

STATUS

approved

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Last modified June 21 16:12 EDT 2018. Contains 305624 sequences. (Running on oeis4.)