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%I #12 Feb 12 2020 18:01:43
%S 0,1,2,2,2,3,3,4,5,6,8,10,13,16,21,27,34,44,56,72,93,119,153,197,254,
%T 327,421,542,698,899,1158,1492,1922,2477,3191,4112,5298,6827,8797,
%U 11335,14606,18821,24252,31251,40269,51890,66864,86160,111024,143064,184350
%N a(n+3) = floor( ( a(n) + 2*a(n+1) + 3*a(n+2) )/4 ), with a(0), a(1), a(2) equal to 0, 1, 2.
%C Ratio of each term to the previous approaches 1.28858..., a root of -4*x^3 + 3*x^2 + 2*x + 1.
%H Andrew Howroyd, <a href="/A074732/b074732.txt">Table of n, a(n) for n = 0..1000</a>
%e a(4) = 2 because ( 1 + 2*2 + 3*2 )/4 = 2.75 and 2.75 floored = 2
%t RecurrenceTable[{a[0]==0,a[1]==1,a[2]==2,a[n]==Floor[(a[n-3]+2a[n-2]+ 3a[n-1])/4]},a,{n,50}] (* _Harvey P. Dale_, May 14 2014 *)
%o (PARI) seq(n)={my(a=vector(n+1)); a[1]=0; a[2]=1; a[3]=2; for(n=1, #a-3, a[n+3] = (a[n] + 2*a[n+1] + 3*a[n+2])\4); a} \\ _Andrew Howroyd_, Feb 12 2020
%Y Cf. A074733.
%K nonn,easy
%O 0,3
%A _Axel Harvey_, Sep 05 2002
%E Terms a(41) and beyond from _Andrew Howroyd_, Feb 12 2020
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