A084627 a(n) = floor(C(n+6,6)/C(n+3,3)).

1, 1, 2, 4, 6, 8, 11, 14, 18, 22, 28, 34, 40, 48, 57, 66, 77, 88, 101, 115, 130, 146, 163, 182, 203, 224, 248, 272, 299, 327, 357, 388, 421, 456, 494, 533, 574, 617, 662, 709, 759, 810, 864, 921, 980, 1041, 1105, 1171, 1240, 1311, 1386, 1463, 1542, 1625, 1711

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. A084626, A084628, A084630, A084631.

Programs

Magma

[Floor(Binomial(n+6,3)/20): n in [0..70]]; // G. C. Greubel, Mar 24 2023

Mathematica

Table[Floor[Binomial[n+6,6]/Binomial[n+3,3]],{n,0,60}] (* Harvey P. Dale, Feb 07 2015 *)
Floor[Binomial[Range[6,76],3]/20] (* G. C. Greubel, Mar 24 2023 *)

SageMath

[binomial(n+6,3)//20 for n in range(71)] # G. C. Greubel, Mar 24 2023

Formula

a(n) = 1 + floor(n*(n^2 +15*n +74)/120).

a(n) = floor(binomial(n+6,3)/20). - G. C. Greubel, Mar 24 2023