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%I #13 Oct 25 2020 08:52:07
%S 5,19,11,35,79,149,251,391,575,809,1099,1451,1871,2365,2939,3599,4351,
%T 5201,6155,7219,8399,9701,11131,12695,14399,16249,18251,20411,22735,
%U 25229,27899,30751,33791,37025,40459,44099,47951,52021,56315,60839,65599,70601,75851
%N Least j > 1 for n > 0 such that j^2 = (n^2 + 1)*(k^2) + (n^2 + 1)*k + 1 where k sequence = A106230.
%C For j^2 = (n^2 + 1)*(k^2) + (n^2 + 1)*k + 1, there is a sequence j(i,n) with a recurrence.
%C For n=1, j(1,1) = 1, j(2,1) = 5, j(i,1) = 6*j(i-1,1) - j(i-2,1).
%C For n=2, j(1,2) = 1, j(2,2) = 19, j(i,2) = 18*j(i-1,2) - j(i-2,2).
%C For n>2, j(1,n) = 1, j(2,n) = n^3 - 2*n^2 + n - 1, j(3,n) = n^3 + 2*n^2 + n + 1, j(4,n) = (4*n^2 + 2)*j(2,n) + 1 then j(i,n) = (4*n^2+2)*j(i-2,n) - j(i-4,n).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F For n > 2, a(n) = n^3 - 2*n^2 + n - 1.
%t LinearRecurrence[{4,-6,4,-1},{5,19,11,35,79,149},43] (* _Georg Fischer_, Oct 25 2020 *)
%o (PARI) a(n) = if(n<3, 14*n-9, n^3-2*n^2+n-1); \\ _Jinyuan Wang_, Apr 07 2020
%Y Cf. A003777, A005563, A005899, A106230.
%K nonn,easy
%O 1,1
%A _Pierre CAMI_, Apr 26 2005
%E More terms from _Jinyuan Wang_, Apr 07 2020
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