A084628 - OEIS

%I #12 Mar 24 2023 10:40:21

%S 1,2,3,6,9,14,20,28,39,52,68,87,110,138,171,209,253,303,361,427,501,

%T 585,678,783,899,1027,1169,1325,1496,1683,1887,2109,2350,2611,2893,

%U 3198,3526,3878,4257,4662,5096,5559,6053,6580,7140,7735,8366,9035,9744,10494

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

%H G. C. Greubel, <a href="/A084628/b084628.txt">Table of n, a(n) for n = 0..5000</a>

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

%F a(n) = floor(binomial(n+7, 4)/35). - _G. C. Greubel_, Mar 24 2023

%t Table[Floor[Binomial[n+7,7]/Binomial[n+3,3]],{n,0,50}]  (* _Harvey P. Dale_, Jan 27 2011 *)

%t Floor[Binomial[Range[7,77],4]/35] (* _G. C. Greubel_, Mar 24 2023 *)

%o (Magma) [Floor(Binomial(n+7,4)/35): n in [0..70]]; // _G. C. Greubel_, Mar 24 2023

%o (SageMath) [binomial(n+7,4)//35 for n in range(71)] # _G. C. Greubel_, Mar 24 2023

%Y Cf. A084627, A084629, A084630, A084631.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jun 01 2003