A165938 a(n) = A002203(n^2) for n>=1.

2, 34, 2786, 1331714, 3710155682, 60245508192802, 5701755387019728962, 3145168096065837266706434, 10111847525912679844192131854786, 189482250299273866835746159841800035874, 20694642381734231604510939638726181796865594402

Offset: 1

Author

Paul D. Hanna, Oct 18 2009

Keywords

• nonn

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..40

Crossrefs

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

Programs

Mathematica

Simplify[Table[(1 + Sqrt[2])^(n^2) + (1 - Sqrt[2])^(n^2), {n, 1, 7}]] (* G. C. Greubel, Apr 18 2016 *)

PARI

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

Formula

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

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

Logarithmic derivative of A165937.