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A211703
a(n) = n + [n/2] + [n/3] + [n/4], where [] = floor.
2
1, 3, 5, 8, 9, 12, 13, 16, 18, 20, 21, 25, 26, 28, 30, 33, 34, 37, 38, 41, 43, 45, 46, 50, 51, 53, 55, 58, 59, 62, 63, 66, 68, 70, 71, 75, 76, 78, 80, 83, 84, 87, 88, 91, 93, 95, 96, 100, 101, 103, 105, 108, 109, 112, 113, 116, 118, 120, 121, 125, 126, 128
OFFSET
1,2
COMMENTS
See A211701 for a discussion and guide to related sequences.
FORMULA
a(n) = a(n-3) + a(n-4) - a(n-7) for n>=8.
G.f.: x*(1 + 3*x + 5*x^2 + 7*x^3 + 5*x^4 + 4*x^5)/((1 - x)^2*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + x^5)). - Ilya Gutkovskiy, Feb 24 2017
MATHEMATICA
f[n_, m_] := Sum[Floor[n/k], {k, 1, m}]
t = Table[f[n, 4], {n, 1, 90}] (* A211703 *)
FindLinearRecurrence[t]
LinearRecurrence[{0, 0, 1, 1, 0, 0, -1}, {1, 3, 5, 8, 9, 12, 13}, 62] (* Ray Chandler, Aug 02 2015 *)
CROSSREFS
Cf. A211701.
Sequence in context: A189130 A189213 A325168 * A274430 A107792 A051206
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 19 2012
STATUS
approved