%I #13 Jul 08 2023 15:49:14
%S 1,2,3,5,7,10,12,14,17,20,23,27,31,36,42,49,57,66,76,88,101,116,133,
%T 153,176,202,232,266,305,350,401,460,527,604,692,793,909,1042,1194,
%U 1368,1568,1797,2059,2359,2703,3097,3548,4065,4657,5335,6112,7002,8021
%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)/6) for n>=6.
%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]/6];
%t Join[{1,2,3,5},RecurrenceTable[{a[4]==7,a[5]==10,a[n]==Floor[a[n-1]+ 1+ a[n-2]/6]},a,{n,60}]] (* _Harvey P. Dale_, Mar 15 2016 *)
%t nxt[{a_,b_}]:={b,Floor[b+1+a/6]}; Join[{1,2,3,5},NestList[nxt,{7,10},50][[;;,1]]] (* _Harvey P. Dale_, Jul 08 2023 *)
%o (PARI) a=concat([1, 2, 3, 5, 7, 10],vector(95));for(i=7,#a,a[i]=1+a[i-1]+a[i-2]\6);a \\ _Charles R Greathouse IV_, Nov 07 2011
%Y Cf. A119592.
%K nonn
%O 0,2
%A _Roger L. Bagula_, May 31 2006
%E More terms from _Zak Seidov_, May 31 2006
%E Edited by _N. J. A. Sloane_, Jun 03 2006