A053618 a(n) = ceiling(binomial(n,4)/n).

0, 0, 0, 1, 1, 3, 5, 9, 14, 21, 30, 42, 55, 72, 91, 114, 140, 170, 204, 243, 285, 333, 385, 443, 506, 575, 650, 732, 819, 914, 1015, 1124, 1240, 1364, 1496, 1637, 1785, 1943, 2109, 2285, 2470, 2665, 2870, 3086, 3311, 3548, 3795, 4054, 4324

Offset: 1

Author

N. J. A. Sloane, Mar 25 2000

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• R. L. Graham and N. J. A. Sloane, Lower bounds for constant weight codes, IEEE Trans. Inform. Theory, 26 (1980), 37-43.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1,-3,3,-1).

Crossrefs

Cf. A007997, A008646, A032192, A053643, A053731, A053733.

Programs

Magma

[Ceiling(Binomial(n,4)/n): n in [1..60]]; // G. C. Greubel, May 16 2019

Mathematica

CoefficientList[Series[x^4*(1-x+x^2)*(1-x+x^2+x^4)/((1-x)^3*(1-x^8)), {x,0,60}], x] (* G. C. Greubel, May 16 2019 *)

PARI

concat([0,0,0], Vec(x^4*(x^2-x+1)*(x^4+x^2-x+1) / ((x-1)^4*(x+1)*(x^2+1)*(x^4+1)) + O(x^60))) \\ Colin Barker, Jan 20 2015

Sage

[ceil(binomial(n,4)/n) for n in (1..60)] # G. C. Greubel, May 16 2019

Formula

a(n) = ( 2*n^3 - 12*n^2 + 22*n - 3 + 9*(-1)^n + 3*(1+(-1)^n)*(-1)^(n*(n-1)/2) - 6*(1 + (-1)^n)*(-1)^floor(n/4) )/48. - Luce ETIENNE, Jan 20 2015

G.f.: x^4*(1 - x + x^2)*(1 - x + x^2 + x^4)/((1-x)^3*(1-x^8)). - Colin Barker, Jan 20 2015