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A173510 a(n) = a(n-1) + a(n-2) - floor( a(n-1)/2 ).

%I A173510 #13 Jul 05 2025 09:56:03
%S A173510 2,1,3,3,5,6,8,10,13,17,22,28,36,46,59,76,97,125,160,205,263,337,432,
%T A173510 553,709,908,1163,1490,1908,2444,3130,4009,5135,6577,8424,10789,13819,
%U A173510 17699,22669,29034,37186,47627,61000,78127,100064,128159,164144,210231,269260,344861,441691
%N A173510 a(n) = a(n-1) + a(n-2) - floor( a(n-1)/2 ).
%C A173510 The limiting ratio a(n+1)/a(n)is:1.2807764064
%t A173510 l[0] = 2; l[1] = 1;
%t A173510 l[n_] := l[n] = l[n - 1] + l[n - 2] - Floor[l[n - 1]/2]
%t A173510 Table[l[n], {n, 0, 30}]
%t A173510 RecurrenceTable[{a[0]==2,a[1]==1,a[n]==a[n-1]+a[n-2]-Floor[a[n-1]/2]},a,{n,50}] (* _Harvey P. Dale_, Sep 03 2013 *)
%o A173510 (Maxima) A173510[n] := block(
%o A173510         if equal(n,0) then return(2) ,
%o A173510         if equal(n,1) then return(1)
%o A173510         else
%o A173510         return(ev(A173510[n-1]+A173510[n-2]-floor(A173510[n-1]/2)))
%o A173510 )$ /* _R. J. Mathar_, Mar 11 2012 */
%Y A173510 Cf. A000032.
%K A173510 nonn
%O A173510 0,1
%A A173510 _Roger L. Bagula_, Nov 23 2010