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 A008859 a(n) = Sum_{k=0..6} binomial(n,k). 18
 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 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 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 and 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 June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)