A053643 a(n) = ceiling(binomial(n,6)/n).
0, 0, 0, 0, 0, 1, 1, 4, 10, 21, 42, 77, 132, 215, 334, 501, 728, 1032, 1428, 1938, 2584, 3392, 4389, 5609, 7084, 8855, 10964, 13455, 16380, 19793, 23751, 28319, 33563, 39556, 46376, 54106, 62832, 72650, 83657, 95960, 109668, 124900
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- R. L. Graham and N. J. A. Sloane, Lower bounds for constant weight codes, IEEE Trans. Inform. Theory, 26 (1980), 37-43.
- Index entries for linear recurrences with constant coefficients, 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).
Programs
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Magma
[Ceiling(Binomial(n,6)/n) : n in [1..50]]; // Wesley Ivan Hurt, Nov 01 2015
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Maple
seq(ceil(binomial(n,5)/6), n=0..50); # Zerinvary Lajos, Jan 12 2009
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Mathematica
Table[Ceiling[Binomial[n, 6]/n], {n, 50}] (* Michael De Vlieger, Nov 01 2015 *) -
PARI
vector(50, n, ceil(binomial(n, 6)/n)) \\ Altug Alkan, Nov 01 2015
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Sage
[ceil(binomial(n,6)/n) for n in (1..50)] # G. C. Greubel, May 17 2019
Formula
From Robert Israel, Nov 01 2015: (Start)
a(n) = ceiling(A000389(n-1)/6).
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)).
(End)