(MAGMAMagma) I:=[0, 21, 504, 597, 704, 3441, 3980]; [n le 7 select I[n] else Self(n-1) + 6*Self(n-3) - 6*Self(n-4) - Self(n-6) + Self(n-7): n in [1..50]]; // G. C. Greubel, Mar 31 2018
_Mohamed Bouhamida (bhmd95(AT)yahoo.fr), _, Jun 14 2007
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x+199)^2 = y^2.
lim_Lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_Lim_{n -> infinity} a(n)/a(n-1) = (201+20*sqrt(2))/199 for n mod 3 = {1, 2}.
lim_Lim_{n -> infinity} a(n)/a(n-1) = (91443+58282*sqrt(2))/199^2 for n mod 3 = 0.
a(n) = 6*a(n-3) - a(n-6) + 398 for n > 6; a(1)=0, a(2)=21, a(3)=504, a(4)=597, a(5)=704, a(6)=3441.
a(1)=0, a(2)=21, a(3)=504, a(4)=597, a(5)=704, a(6)=3441, a(7)=3980, a(n)=a(n-1)+6*a(n-3)-6*a(n-4)-a(n-6)+a(n-7) From _. - _Harvey P. Dale_, Jun 03 2012
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G. C. Greubel, <a href="/A129993/b129993.txt">Table of n, a(n) for n = 1..1000</a>
a(n) = 6*a(n-3) -a(n-6) +398 for n > 6; a(1)=0, a(2)=21, a(3)=504, a(4)=597, a(5)=704, a(6)=3441.
(PARI) {forstep(n=0, 500000000, [1, 3], if(issquare(2*n^2+398*n+39601), print1(n, ", ")))};
(MAGMA) I:=[0, 21, 504, 597, 704, 3441, 3980]; [n le 7 select I[n] else Self(n-1) + 6*Self(n-3) - 6*Self(n-4) - Self(n-6) + Self(n-7): n in [1..50]]; // G. C. Greubel, Mar 31 2018
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<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).
<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).
<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).