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A073352 Positive integers making n^2*(n-1)*(2*n-1)^2*(7*n-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

G. C. Greubel, Table of n, a(n) for n = 0..825

Index entries for linear recurrences with constant coefficients, signature (17,-17,1).

FORMULA

G.f.: (1 - 13*x + 4*x^2)/((1-x)*(1-16*x+x^2)).

a(n) = 16*a(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 + (8+3*sqrt(7))^n ), with n>=0 - Paolo P. Lava, Jun 19 2008

a(n) = (4 + 3*ChebyshevU(n, 8) - 24*ChebyshevU(n-1, 8))/7. - G. C. Greubel, Feb 09 2020

EXAMPLE

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

MAPLE

seq( simplify((4 +3*ChebyshevU(n, 8) -24*ChebyshevU(n-1, 8))/7), n=0..30); # G. C. Greubel, Feb 09 2020

MATHEMATICA

LinearRecurrence[{17, -17, 1}, {1, 4, 55}, 30] (* Harvey P. Dale, Dec 09 2018 *)

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}

(MAGMA) I:=[1, 4, 55]; [n le 3 select I[n] else 17*Self(n-1) - 17*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 09 2020

(Sage) [(4 +3*chebyshev_U(n, 8) -24*chebyshev_U(n-1, 8))/7 for n in (0..30)] # G. C. Greubel, Feb 09 2020

(GAP) a:=[1, 4, 55];; for n in [4..30] do a[n]:=17*a[n-1]-17*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Feb 09 2020

CROSSREFS

Cf. A007750, A077412.

Sequence in context: A204107 A285366 A202163 * A258793 A195634 A322627

Adjacent sequences:  A073349 A073350 A073351 * A073353 A073354 A073355

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 27 2002

STATUS

approved

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Last modified July 8 04:16 EDT 2020. Contains 335504 sequences. (Running on oeis4.)