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 A116082 #38 Apr 02 2024 23:05:27
%S A116082 0,1,3,7,15,31,63,127,254,501,967,1815,3301,5811,9907,16383,26332,
%T A116082 41225,63003,94183,137979,198439,280599,390655,536154,726205,971711,
%U A116082 1285623,1683217,2182395,2804011,3572223,4514872,5663889,7055731,8731847
%N A116082 a(n) = C(n,7) + C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
%C A116082 Number of compositions with at most three parts distinct from 1 and with a sum at most n. - _Beimar Naranjo_, Mar 12 2024
%H A116082 Vincenzo Librandi, <a href="/A116082/b116082.txt">Table of n, a(n) for n = 0..1000</a>
%H A116082 Michael Boardman, <a href="http://www.jstor.org/stable/3219201">The Egg-Drop Numbers</a>, Mathematics Magazine, 77 (2004), 368-372. See Table 2 on page 370. [_Parthasarathy Nambi_, Jun 18 2009]
%H A116082 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A116082 a(n) = A000580(n) + A000579(n) + A000389(n) + A000332(n) + A000292(n) + A000217(n) + n.
%F A116082 a(n) = A000580(n) + A115567(n).
%F A116082 a(n) = n*(n^6 - 14*n^5 + 112*n^4 - 350*n^3 + 1099*n^2 + 364*n + 3828)/5040. - _Emeric Deutsch_, Apr 14 2006
%F A116082 G.f.: x*(1 - 5*x + 11*x^2 - 13*x^3 + 9*x^4 - 3*x^5 + x^6)/(1-x)^8. - _R. J. Mathar_, Jun 20 2011
%F A116082 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8), with a(0)=0, a(1)=1, a(2)=3, a(3)=7, a(4)=15, a(5)=31, a(6)=63, a(7)=127. - _Harvey P. Dale_, Aug 05 2011
%p A116082 a:=n->n*(n^6-14*n^5+112*n^4-350*n^3+1099*n^2+364*n+3828)/5040: seq(a(n),n=0..35); # _Emeric Deutsch_, Apr 14 2006
%p A116082 seq(sum(binomial(n,k),k=1..7),n=0..35); # _Zerinvary Lajos_, Dec 14 2007
%t A116082 Table[Total[Binomial[n,Range[7]]],{n,0,40}] (* or *) LinearRecurrence[ {8,-28,56,-70,56,-28,8,-1},{0,1,3,7,15,31,63,127},41](* _Harvey P. Dale_, Aug 05 2011 *)
%o A116082 (Magma) [n*(n^6-14*n^5+112*n^4-350*n^3+1099*n^2+364*n+3828)/5040: n in [0..40]]; // _Vincenzo Librandi_, Jun 21 2011
%o A116082 (PARI) for(n=0,30, print1(n*(n^6 -14*n^5 +112*n^4 -350*n^3 +1099*n^2 +364*n +3828)/5040, ", ")) \\ _G. C. Greubel_, Nov 25 2017
%Y A116082 Cf. A000217, A000225, A004006, A055795, A057703, A115567, A116082. [_Parthasarathy Nambi_, Jun 18 2009]
%K A116082 easy,nonn
%O A116082 0,3
%A A116082 _Jonathan Vos Post_, Mar 13 2006