|
%I #24 Feb 27 2024 03:00:11
%S 1,4,55,868,13825,220324,3511351,55961284,891869185,14213945668,
%T 226531261495,3610286238244,57538048550401,916998490568164,
%U 14614437800540215,232914006318075268,3712009663288664065
%N Positive integers making n^2*(n-1)*(2*n-1)^2*(7*n-1)/36 a square.
%H G. C. Greubel, <a href="/A073352/b073352.txt">Table of n, a(n) for n = 0..825</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-17,1).
%F G.f.: (1 - 13*x + 4*x^2)/((1-x)*(1-16*x+x^2)).
%F a(n) = (4 + 3*ChebyshevU(n, 8) - 24*ChebyshevU(n-1, 8))/7. - _G. C. Greubel_, Feb 09 2020
%e G.f. = 1 + 4*x + 55*x^2 + 868*x^3 + 13825*x^4 + 220324*x^5 + 3511351*x^6 + ...
%p seq( simplify((4 +3*ChebyshevU(n,8) -24*ChebyshevU(n-1,8))/7), n=0..30); # _G. C. Greubel_, Feb 09 2020
%t LinearRecurrence[{17,-17,1},{1,4,55},30] (* _Harvey P. Dale_, Dec 09 2018 *)
%o (PARI) {a(n) = if( n<0, a(-n), if( n<1, 1, 16*a(n-1) - a(n-2) - 8))}
%o (PARI) {a(n) = (4 + 3 * real((8 + 3 * quadgen(28))^n)) / 7}
%o (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
%o (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
%o (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
%Y Cf. A007750, A077412.
%K nonn
%O 0,2
%A _Michael Somos_, Jul 27 2002
|
