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A008859
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a(n) = Sum_{k=0..6} binomial(n,k).
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17
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1, 2, 4, 8, 16, 32, 64, 127, 247, 466, 848, 1486, 2510, 4096, 6476, 9949, 14893, 21778, 31180, 43796, 60460, 82160, 110056, 145499, 190051, 245506, 313912, 397594, 499178, 621616, 768212, 942649, 1149017, 1391842, 1676116, 2007328
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OFFSET
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0,2
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COMMENTS
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a(n) is the maximal number of regions in 6-space formed by n-1 5-dimensional hypercubes. - Christian Schroeder, Jan 04 2016
a(n) is the number of binary words of length n matching the regular expression 0*1*0*1*0*1*0*. A000124, A000125, A000127, A006261 count binary words of the form 0*1*0*, 1*0*1*0*, 0*1*0*1*0*, and 1*0*1*0*1*0*, respectively. - Manfred Scheucher, Jun 22 2023
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..3} binomial(n+1, 2*k). - Len Smiley, Oct 20 2001
O.g.f.: (1 - 5*x + 11*x^2 - 13*x^3 + 9*x^4 - 3*x^5 + x^6)/(1-x)^7. - R. J. Mathar, Apr 02 2008
a(n) = (n^6 - 9*n^5 + 55*n^4 - 75*n^3 + 304*n^2 + 444*n + 720)/720. - Gerry Martens , May 04 2016
E.g.f.: (720 + 720*x + 360*x^2 + 120*x^3 + 30*x^4 + 6*x^5 + x^6)*exp(x)/6!. - Ilya Gutkovskiy, May 04 2016
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MAPLE
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add(binomial(n, k), k=0..6) ;
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MATHEMATICA
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Table[Sum[Binomial[n, k], {k, 0, 6}], {n, 0, 40}] (* Harvey P. Dale, Jan 16 2012 *)
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PROG
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(Haskell)
(Magma) [(&+[Binomial(n, k): k in [0..6]]): n in [0..40]]; // G. C. Greubel, Sep 13 2019
(Sage) [sum(binomial(n, k) for k in (0..6)) for n in (0..40)] # G. C. Greubel, Sep 13 2019
(GAP) List([0..40], n-> Sum([0..6], k-> Binomial(n, k)) ); # G. C. Greubel, Sep 13 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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