A211703 a(n) = n + [n/2] + [n/3] + [n/4], where [] = floor.

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

Author

Clark Kimberling, Apr 19 2012

Keywords

• nonn

Comments

See A211701 for a discussion and guide to related sequences.

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 1, 0, 0, -1).

Crossrefs

Cf. A211701.

Programs

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 *)

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