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%I #12 Sep 08 2022 08:45:33
%S 1,3,9,31,97,308,969,3051,9601,30210,95049,299052,940897,2960313,
%T 9313929,29304086,92198401,290080547,912670089,2871501385,9034502497,
%U 28424933309,89432354889,281377831710,885289046401,2785353383794,8763458109129,27572156006234
%N a(n) = floor((sqrt(2) + sqrt(3))^n).
%H G. C. Greubel, <a href="/A138281/b138281.txt">Table of n, a(n) for n = 0..1000</a>
%F a(2*n) = floor(A001079(n) + A001078(n)*sqrt(6));
%F (sqrt(2) + sqrt(3))^(2*n) = A001079(n) + A001078(n)*sqrt(6);
%F a(2*n+1) = floor(A054320(n)*sqrt(2) + A138288(n)*sqrt(3));
%F (sqrt(2)+sqrt(3))^(2*n+1) = A054320(n)*sqrt(2) + A138288(n)*sqrt(3).
%t Table[Floor[(Sqrt[2] + Sqrt[3])^n], {n, 0, 50}] (* _G. C. Greubel_, Jan 27 2018 *)
%o (PARI) for(n=0,50, print1(floor((sqrt(2) + sqrt(3))^n), ", ")) \\ _G. C. Greubel_, Jan 27 2018
%o (Magma) [Floor((Sqrt(2) + Sqrt(3))^n): n in [0..50]]; // _G. C. Greubel_, Jan 27 2018
%Y Cf. A089078, A110117, A121503, A135611, A135798.
%K nonn
%O 0,2
%A _Reinhard Zumkeller_, Mar 12 2008
%E Terms a(16) and a(18) corrected, terms a(19) onward added by _G. C. Greubel_, Jan 27 2018
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