A138281 a(n) = floor((sqrt(2) + sqrt(3))^n).

1, 3, 9, 31, 97, 308, 969, 3051, 9601, 30210, 95049, 299052, 940897, 2960313, 9313929, 29304086, 92198401, 290080547, 912670089, 2871501385, 9034502497, 28424933309, 89432354889, 281377831710, 885289046401, 2785353383794, 8763458109129, 27572156006234

Offset: 0

Author

Reinhard Zumkeller, Mar 12 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A089078, A110117, A121503, A135611, A135798.

Programs

Magma

[Floor((Sqrt(2) + Sqrt(3))^n): n in [0..50]]; // G. C. Greubel, Jan 27 2018

Mathematica

Table[Floor[(Sqrt[2] + Sqrt[3])^n], {n, 0, 50}] (* G. C. Greubel, Jan 27 2018 *)

PARI

for(n=0,50, print1(floor((sqrt(2) + sqrt(3))^n), ", ")) \\ G. C. Greubel, Jan 27 2018

Formula

a(2*n) = floor(A001079(n) + A001078(n)*sqrt(6));

(sqrt(2) + sqrt(3))^(2*n) = A001079(n) + A001078(n)*sqrt(6);

a(2*n+1) = floor(A054320(n)*sqrt(2) + A138288(n)*sqrt(3));

(sqrt(2)+sqrt(3))^(2*n+1) = A054320(n)*sqrt(2) + A138288(n)*sqrt(3).

Extensions

Terms a(16) and a(18) corrected, terms a(19) onward added by G. C. Greubel, Jan 27 2018