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A008859 a(n) = Sum_{k=0..6} C(n,k). 16
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the maximal number of regions in 6-space formed by n-1 5-dimensional hypercubes. - Christian Schroeder, Jan 04 2016

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

a(n) = sum(binomial(n+1, 2k), k=0..3). - 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) = a(n-1) + A006261(n-1). - Christian Schroeder, Jan 04 2016

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)/720. - Ilya Gutkovskiy, May 04 2016

MAPLE

A008859 := proc(n)

    add(binomial(n, k), k=0..6) ;

end proc: # R. J. Mathar, Oct 30 2015

MATHEMATICA

Table[Sum[Binomial[n, k], {k, 0, 6}], {n, 0, 40}] (* Harvey P. Dale, Jan 16 2012 *)

PROG

(Haskell)

a008859 = sum . take 7 . a007318_row  -- Reinhard Zumkeller, Nov 24 2012

(PARI) a(n)=sum(k=0, 6, binomial(n, k)) \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A008860, A008861, A008862, A008863, A006261, A000127, A007318, A219531.

Sequence in context: A258585 A235701 A054044 * A145113 A062257 A208127

Adjacent sequences:  A008856 A008857 A008858 * A008860 A008861 A008862

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and R. K. Guy

STATUS

approved

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Last modified December 15 01:00 EST 2017. Contains 296020 sequences.