A074733 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.

0, 1, 2, 3, 4, 6, 8, 12, 17, 25, 36, 53, 77, 112, 164, 239, 349, 510, 745, 1089, 1592, 2327, 3401, 4971, 7266, 10621, 15525, 22693, 33171, 48486, 70873, 103597, 151430, 221348, 323549, 472939, 691305, 1010496, 1477065, 2159059, 3155945, 4613116, 6743096

Offset

0,3

Comments

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.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A074732.

Sequence in context: A342338 A221942 A107368 * A001461 A048597 A332839

Adjacent sequences: A074730 A074731 A074732 * A074734 A074735 A074736

Keyword

easy,nonn

Author

Axel Harvey, Sep 05 2002

Extensions

Terms a(31) and beyond from Andrew Howroyd, Feb 12 2020

Status

approved