A084628 a(n) = floor(binomial(n+7,7)/binomial(n+3,3)).

1, 2, 3, 6, 9, 14, 20, 28, 39, 52, 68, 87, 110, 138, 171, 209, 253, 303, 361, 427, 501, 585, 678, 783, 899, 1027, 1169, 1325, 1496, 1683, 1887, 2109, 2350, 2611, 2893, 3198, 3526, 3878, 4257, 4662, 5096, 5559, 6053, 6580, 7140, 7735, 8366, 9035, 9744, 10494

Offset: 0

Author

Paul Barry, Jun 01 2003

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A084627, A084629, A084630, A084631.

Programs

Magma

[Floor(Binomial(n+7,4)/35): n in [0..70]]; // G. C. Greubel, Mar 24 2023

Mathematica

Table[Floor[Binomial[n+7,7]/Binomial[n+3,3]],{n,0,50}]  (* Harvey P. Dale, Jan 27 2011 *)
Floor[Binomial[Range[7,77],4]/35] (* G. C. Greubel, Mar 24 2023 *)

SageMath

[binomial(n+7,4)//35 for n in range(71)] # G. C. Greubel, Mar 24 2023

Formula

a(n) = 1 + floor( n*(n+11)*(n^2 +11*n +58)/840 ).

a(n) = floor(binomial(n+7, 4)/35). - G. C. Greubel, Mar 24 2023