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a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=7, a(5)=10; a(n) = floor(a(n-1) + 1 + (a(n-2) + 1)/6) for n>=6.
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%I #8 May 12 2024 19:25:46

%S 1,2,3,5,7,10,12,14,17,20,24,28,33,38,44,51,59,68,79,91,105,121,139,

%T 160,184,211,242,278,319,366,420,482,553,634,727,833,955,1095,1255,

%U 1438,1648,1888,2163,2478,2839,3253,3727,4270,4892,5604,6420,7355,8426

%N a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=7, a(5)=10; a(n) = floor(a(n-1) + 1 + (a(n-2) + 1)/6) for n>=6.

%C A variant of A119565.

%t a[0]=1; a[1]=2; a[2]=3; a[3]=5; a[4]=7; a[5]=10; a[n_]:=a[n]=Floor[a[n-1]+1+(a[n-2]+1)/6];Array[a, 30]

%t NestList[nxt, {7, 10}, 10][[;; , 1]]; Join[{1,2,3,5},NestList[nxt,{7,10},50][[;;,1]]] (* _Harvey P. Dale_, May 12 2024 *)

%Y Cf. A119565.

%K nonn

%O 0,2

%A _Zak Seidov_, Jun 01 2006

%E Edited by _Dean Hickerson_, Jun 03 2006

%E First Mathematica program corrected by _Harvey P. Dale_, May 12 2024