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%I #24 Aug 27 2017 12:50:19
%S 1,1,3,5,10,19,36,69,131,251,478,913,1741,3322,6338,12092,23070,44014,
%T 83972,160206,305650,583135,1112536,2122555,4049524,7725897,14739878,
%U 28121524,53651742,102359650,195287193,372579307,710826647,1356152937,2587340805
%N a(1) = a(2) = 1; a(n+1) = round( a(n) + sqrt(3)*a(n-1) ).
%H Bruno Berselli, <a href="/A133999/b133999.txt">Table of n, a(n) for n = 1..1000</a>
%e a(7) = 36 because a(6) is 19 and sqrt(3)*a(5) = 17.32, round(19+17.32) = 36
%t RecurrenceTable[{a[0] == a[1] == 1, a[n] == Floor[a[n - 1] + Sqrt[3] a[n - 2] + 1/2]}, a[n], {n, 0, 40}] (* _Bruno Berselli_, Mar 25 2014 *)
%t nxt[{a_,b_}]:={b,Round[b+a*Sqrt[3]]}; NestList[nxt,{1,1},40][[All,1]] (* _Harvey P. Dale_, Aug 27 2017 *)
%o (PARI) lista(nn) = {va = vector(nn); va[1] = 1; va[2] = 1; print1(va[1], ", ", va[2], ", "); for (n=3, nn, va[n] = round(va[n-1] + sqrt(3)*va[n-2]); print1(va[n], ", "););} \\ _Michel Marcus_, Mar 24 2014
%K nonn,easy
%O 1,3
%A _Ben Paul Thurston_, Jan 09 2008
%E More terms from _Michel Marcus_, Mar 24 2014