A084626 a(n) = floor(C(n+6,6)/C(n+2,2)).

1, 2, 4, 8, 14, 22, 33, 47, 66, 91, 121, 158, 204, 258, 323, 399, 487, 590, 708, 843, 996, 1170, 1365, 1583, 1827, 2097, 2397, 2728, 3091, 3490, 3927, 4403, 4921, 5483, 6092, 6751, 7462, 8227, 9050, 9933, 10879, 11891, 12972, 14125, 15353, 16660, 18048

Offset: 0

Author

Paul Barry, Jun 01 2003

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A011865, A084624, A084627, A084628, A084630, A084631.

Programs

Magma

[Floor(n*(n+9)*(n^2+9*n+38)/360)+1: n in [0..50]]; // Vincenzo Librandi, Aug 02 2013

Mathematica

Table[Floor[n*(n+9)*(n^2+9*n+38)/360] +1, {n,0,50}] (* Vincenzo Librandi, Aug 02 2013 *)
Floor[Binomial[Range[6,76],4]/15] (* G. C. Greubel, Mar 24 2023 *)

SageMath

[binomial(n+6,4)//15 for n in range(71)] # G. C. Greubel, Mar 24 2023

Formula

a(n) = 1 + floor( n*(n+9)*(n^2 +9*n +38)/360 ).

a(n) = floor(binomial(n+6,4)/15). - G. C. Greubel, Mar 24 2023