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a(n) = floor(((1+sqrt(2))/2)^n).
1

%I #8 Sep 08 2022 08:45:29

%S 1,1,1,2,2,3,3,4,5,6,7,9,11,13,16,20,24,29,35,43,52,62,75,91,110,133,

%T 161,194,234,283,342,412,498,601,726,876,1058,1277,1541,1861,2246,

%U 2712,3273,3951,4770,5758,6951,8390,10128,12226,14758,17814,21504,25957

%N a(n) = floor(((1+sqrt(2))/2)^n).

%H G. C. Greubel, <a href="/A125894/b125894.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[Floor[((1 + Sqrt[2])/2)^n], {n, 1, 100}]

%o (PARI) vector(100, n, floor(((1+sqrt(2))/2)^n)) \\ _G. C. Greubel_, Oct 02 2018

%o (Magma) [Floor(((1+Sqrt(2))/2)^n): n in [1..100]]; // _G. C. Greubel_, Oct 02 2018

%Y Cf. A125890-A125899.

%Y Cf. A174968 ((1+sqrt(2))/2).

%K nonn

%O 1,4

%A _Artur Jasinski_, Dec 13 2006