%I #10 Apr 18 2016 02:58:09

%S 2,34,2786,1331714,3710155682,60245508192802,5701755387019728962,

%T 3145168096065837266706434,10111847525912679844192131854786,

%U 189482250299273866835746159841800035874,20694642381734231604510939638726181796865594402

%N a(n) = A002203(n^2) for n>=1.

%H Paul D. Hanna, <a href="/A165938/b165938.txt">Table of n, a(n) for n = 1..40</a>

%F a(n) == 2 (mod 32).

%F a(n) = (1+sqrt(2))^(n^2) + (1-sqrt(2))^(n^2).

%F Logarithmic derivative of A165937.

%t Simplify[Table[(1 + Sqrt[2])^(n^2) + (1 - Sqrt[2])^(n^2), {n, 1, 7}]] (* _G. C. Greubel_, Apr 18 2016 *)

%o (PARI) {a(n)=polcoeff(2*(1-x)/(1-2*x-x^2 +x*O(x^(n^2))),n^2)}

%Y Cf. A165937, A002203, A000129 (Pell numbers).

%K nonn

%O 1,1

%A _Paul D. Hanna_, Oct 18 2009