This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A084624 #13 Mar 24 2023 17:51:28
%S A084624 1,2,3,5,8,12,16,22,28,36,45,56,68,81,96,114,133,154,177,202,230,260,
%T A084624 292,327,365,406,449,496,545,598,654,714,777,843,913,988,1066,1148,
%U A084624 1234,1324,1419,1518,1621,1729,1842,1960,2082,2210,2342,2480,2623,2772,2926
%N A084624 a(n) = floor(C(n+5,5)/C(n+2,2)).
%H A084624 G. C. Greubel, <a href="/A084624/b084624.txt">Table of n, a(n) for n = 0..5000</a>
%H A084624 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).
%F A084624 a(n) = 1 + floor( n*(n^2 + 12*n + 47)/60 ).
%F A084624 From _G. C. Greubel_, Mar 24 2023: (Start)
%F A084624 a(n) = floor( binomial(n+5,3)/10 ).
%F A084624 G.f.: (1 -x +x^3 -x^6 +2*x^7 -2*x^8 +2*x^9 -x^10 +x^11 -x^12 +x^14 +x^15 -2*x^16 +x^17)/((1-x)^3*(1-x^20)). (End)
%t A084624 LinearRecurrence[{3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1},{1,2,3, 5,8,12,16,22,28,36,45,56,68,81,96,114,133,154,177,202,230, 260,292},53] (* _Ray Chandler_, Jul 17 2015 *)
%t A084624 Table[Floor[Binomial[n+5,5]/Binomial[n+2,2]],{n,0,60}] (* or *) Table[ Floor[((3+n)(4+n)(5+n))/60],{n,0,60}] (* _Harvey P. Dale_, Sep 04 2017 *)
%t A084624 Floor[Binomial[Range[5,65],3]/10] (* _G. C. Greubel_, Mar 24 2023 *)
%o A084624 (Magma) [Floor(Binomial(n+5,3)/10): n in [0..60]]; // _G. C. Greubel_, Mar 24 2023
%o A084624 (SageMath) [(binomial(n+5,3)//10) for n in range(61)] # _G. C. Greubel_, Mar 24 2023
%Y A084624 Cf. A011865, A084625, A084626, A084627, A084628, A084630, A084631.
%K A084624 easy,nonn
%O A084624 0,2
%A A084624 _Paul Barry_, Jun 01 2003