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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

Ângela Mestre, José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.

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

FORMULA

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) = 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)/6!. - 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

(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

CROSSREFS

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

Sequence in context: A235701 A054044 A325741 * A335247 A145113 A062257

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 November 29 16:39 EST 2022. Contains 358431 sequences. (Running on oeis4.)