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A053643 a(n) = ceiling(binomial(n,6)/n).

%I A053643 #46 Feb 26 2025 11:06:16
%S A053643 0,0,0,0,0,1,1,4,10,21,42,77,132,215,334,501,728,1032,1428,1938,2584,
%T A053643 3392,4389,5609,7084,8855,10964,13455,16380,19793,23751,28319,33563,
%U A053643 39556,46376,54106,62832,72650,83657,95960,109668,124900
%N A053643 a(n) = ceiling(binomial(n,6)/n).
%H A053643 Robert Israel, <a href="/A053643/b053643.txt">Table of n, a(n) for n = 1..10000</a>
%H A053643 R. L. Graham and N. J. A. Sloane, <a href="http://dx.doi.org/10.1109/TIT.1980.1056141">Lower bounds for constant weight codes</a>, IEEE Trans. Inform. Theory, 26 (1980), 37-43.
%H A053643 <a href="/index/Rec#order_59">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1,0,0,0,0,0,0,0,0,0,0,0,0,1,-5,10,-10,5,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,5,-10,10,-5,1,0,0,0,0,0,0,0,0,0,0,0,0,1,-5,10,-10,5,-1).
%F A053643 From _Robert Israel_, Nov 01 2015: (Start)
%F A053643 a(n) = ceiling(A000389(n-1)/6).
%F A053643 G.f.: (x^52 -2*x^51 +4*x^50 -4*x^49 +2*x^48 +x^47 -x^46 +2*x^44 -2*x^43 +x^42 -x^41 +4*x^40 -5*x^39 +4*x^38 -2*x^37 +3*x^36 -5*x^35 +5*x^34 -2*x^33 -2*x^32 +5*x^31 -5*x^30 +2*x^29 +2*x^28 -5*x^27 +5*x^26 -2*x^25 -2*x^24 +5*x^23 -5*x^22 +2*x^21 +2*x^20 -5*x^19 +5*x^18 -3*x^17 +4*x^16 -7*x^15 +9*x^14 -7*x^13 +5*x^12 -4*x^11 +4*x^10 -2*x^9 +3*x^7 -4*x^6 +x^5 +6*x^4 -10*x^3 +9*x^2 -4*x +1)*x^6/((x -1)^6*(x +1)*(x^4 +1)*(x^2 +x +1)*(x^2 -x +1)*(x^6 +x^3 +1)*(x^6 -x^3 +1)*(x^8 -x^4 +1)*(x^24 -x^12 +1)).
%F A053643 (End)
%p A053643 seq(ceil(binomial(n,5)/6), n=0..50); # _Zerinvary Lajos_, Jan 12 2009
%t A053643 Table[Ceiling[Binomial[n, 6]/n], {n, 50}] (* _Michael De Vlieger_, Nov 01 2015 *)
%o A053643 (PARI) vector(50, n, ceil(binomial(n, 6)/n)) \\ _Altug Alkan_, Nov 01 2015
%o A053643 (Magma) [Ceiling(Binomial(n,6)/n) : n in [1..50]]; // _Wesley Ivan Hurt_, Nov 01 2015
%o A053643 (Sage) [ceil(binomial(n,6)/n) for n in (1..50)] # _G. C. Greubel_, May 17 2019
%Y A053643 Cf. A000389, A000579, A053618.
%K A053643 nonn,easy
%O A053643 1,8
%A A053643 _N. J. A. Sloane_, Mar 25 2000