cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A106231 Least j > 1 such that j^2 = (4*n^2 + 2)*(k^2) + (4*n^2 + 2)*k + 1.

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%I A106231 #16 Apr 07 2020 08:48:44
%S A106231 11,19,77,199,409,731,1189,1807,2609,3619,4861,6359,8137,10219,12629,
%T A106231 15391,18529,22067,26029,30439,35321,40699,46597,53039,60049,67651,
%U A106231 75869,84727,94249,104459,115381,127039,139457,152659,166669,181511,197209,213787
%N A106231 Least j > 1 such that j^2 = (4*n^2 + 2)*(k^2) + (4*n^2 + 2)*k + 1.
%C A106231 For j there is always a recurrence.
%C A106231 For n=1, j(1,1) = 1, j(2,1) = 10*j(1,1) + 1, then j(i,1) = 10*j(i-1,1) - j(i-3).
%C A106231 For n>1, j(1,n) = 1, j(2,n) = 4*n^3 - 4*n^2 + 2*n - 1, j(3,n) = 4*n^3 + 4*n^2 + 2*n+1, j(4,n) = (8*n^2+2)*j(2,n) + 1 then j(i,n) = (8*n^2+2)*j(i-2) - j(i-4,n).
%H A106231 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A106231 a(1) = 11, a(n) = 4*n^3 - 4*n^2 + 2*n - 1 for n > 1, k sequence = A106232.
%F A106231 G.f.: x*(10*x^4-39*x^3+67*x^2-25*x+11) / (x-1)^4. - _Colin Barker_, Mar 06 2013
%o A106231 (PARI) a(n) = if(n==1, 11, 4*n^3-4*n^2+2*n-1); \\ _Jinyuan Wang_, Apr 07 2020
%Y A106231 Cf. A106232.
%K A106231 nonn,easy
%O A106231 1,1
%A A106231 _Pierre CAMI_, Apr 26 2005
%E A106231 More terms from _Colin Barker_, Mar 06 2013