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.
%I A107075 #25 Nov 15 2018 15:19:59
%S A107075 1,181,58141,18721081,6028129801,1941039074701,625008553923781,
%T A107075 201250813324382641,64802136881897286481,20866086825157601864101,
%U A107075 6718815155563865902953901,2163437614004739663149291881
%N A107075 Centered square numbers that are also centered pentagonal numbers.
%C A107075 The centered square numbers are n^2 + (n+1)^2 while the centered pentagonal numbers are (5*r^2 + 5*r + 2)/2. A number has both properties iff 5*(2*r+1)^2 = (4*n+2)^2 + 1. We solve the equation 5*Y^2 - 1 = X^2 whose solutions in positive integers are given by A075796 and A007805 respectively. The r values are 0,8,..., i.e., A053606. The n values define A119032.
%H A107075 Harvey P. Dale, <a href="/A107075/b107075.txt">Table of n, a(n) for n = 1..399</a>
%H A107075 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (323,-323,1).
%F A107075 G.f.: (z*(1-142*z+z^2))/((1-z)*(1-322*z+z^2)).
%F A107075 a(n+2) = 322*a(n+1)-a(n)-140 with a(1)=1 and a(2)=181.
%F A107075 a(n+1) = 161*a(n)-70+18*(80*a(n)^2-70*a(n)+15)^0.5.
%F A107075 a(n) = (14+(9-4*sqrt(5))^(2*n-1)+(9+4*sqrt(5))^(2*n-1))/32. - _Gerry Martens_, Jun 06 2015
%p A107075 a:= n-> (Matrix([181,1,1]). Matrix([[323,1,0], [ -323,0,1], [1,0,0]])^n)[1,3]: seq(a(n), n=1..20); # _Alois P. Heinz_, Aug 14 2008
%t A107075 LinearRecurrence[{323,-323,1},{1,181,58141},20] (* _Harvey P. Dale_, Nov 15 2018 *)
%Y A107075 Cf. A007805, A053606, A075796, A119032.
%K A107075 nonn,easy
%O A107075 1,2
%A A107075 _Richard Choulet_, Aug 30 2007, Sep 20 2007
%E A107075 More terms from _Alois P. Heinz_, Aug 14 2008