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URL: https://oeis.org/A074733

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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.
2
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
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
KEYWORD
easy,nonn
AUTHOR
Axel Harvey, Sep 05 2002
EXTENSIONS
Terms a(31) and beyond from Andrew Howroyd, Feb 12 2020
STATUS
approved