A074733 - OEIS

%I #11 Feb 12 2020 18:01:30

%S 0,1,2,3,4,6,8,12,17,25,36,53,77,112,164,239,349,510,745,1089,1592,

%T 2327,3401,4971,7266,10621,15525,22693,33171,48486,70873,103597,

%U 151430,221348,323549,472939,691305,1010496,1477065,2159059,3155945,4613116,6743096

%N a(n+4) = floor( ( a(n) + 2*a(n+1) + 3*a(n+2) + 4*a(n+3) )/5 ), with a(0), a(1), a(2), a(3) equal to 0, 1, 2, 3.

%C Ratio of each term to the preceding approaches 1.46172263..., a root of -5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1.

%H Andrew Howroyd, <a href="/A074733/b074733.txt">Table of n, a(n) for n = 0..1000</a>

%e a(7) = 12 because (3 + 2*4 + 3*5 + 4*8)/5 = 12.2 and 12.2 floored = 12.

%t Nest[Append[#, Floor@ Total[Range[4] * #[[-4 ;; -1]]/5 ]] &, Range[0, 3], 39] (* _Michael De Vlieger_, Feb 12 2020 *)

%o (PARI) seq(n)={my(a=vector(n+1)); a[1]=0; a[2]=1; a[3]=2; a[4]=3; for(n=1, #a-4, a[n+4] = (a[n] + 2*a[n+1] + 3*a[n+2] + 4*a[n+3])\5); a} \\ _Andrew Howroyd_, Feb 12 2020

%Y Cf. A074732.

%K easy,nonn

%O 0,3

%A _Axel Harvey_, Sep 05 2002

%E Terms a(31) and beyond from _Andrew Howroyd_, Feb 12 2020