The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A017902 Expansion of 1/(1 - x^8 - x^9 - ...). 4
 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 64, 78, 96, 119, 148, 184, 228, 281, 345, 423, 519, 638, 786, 970, 1198, 1479, 1824, 2247, 2766, 3404, 4190, 5160, 6358, 7837, 9661, 11908, 14674, 18078 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,17 COMMENTS A Lamé sequence of higher order. a(n) = number of compositions of n in which each part is >=8. - Milan Janjic, Jun 28 2010 a(n+8) equals the number of n-length binary words such that 0 appears only in a run which length is a multiple of 8. - Milan Janjic, Feb 17 2015 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 I. M. Gessel, Ji Li, Compositions and Fibonacci identities, J. Int. Seq. 16 (2013) 13.4.5 J. Hermes, Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden, Math. Ann., 45 (1894), 371-380. Augustine O. Munagi, Integer Compositions and Higher-Order Conjugation, J. Int. Seq., Vol. 21 (2018), Article 18.8.5. Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 1). FORMULA G.f.: (x-1)/(x-1+x^8). - Alois P. Heinz, Aug 04 2008 For positive integers n and k such that k <= n <= 8*k, and 7 divides n-k, define c(n,k) = binomial(k,(n-k)/7), and c(n,k) = 0, otherwise. Then, for n>=1, a(n+8) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011 a(n) = A005710(n)-A005710(n-1). - R. J. Mathar, Sep 07 2016 MAPLE f := proc(r) local t1, i; t1 := []; for i from 1 to r do t1 := [op(t1), 0]; od: for i from 1 to r+1 do t1 := [op(t1), 1]; od: for i from 2*r+2 to 50 do t1 := [op(t1), t1[i-1]+t1[i-1-r]]; od: t1; end; # set r = order a:= n-> (Matrix(8, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0\$6, 1][i] else 0 fi)^n)[8, 8]: seq(a(n), n=0..53); # Alois P. Heinz, Aug 04 2008 MATHEMATICA LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0}, 60] (* Jean-François Alcover, Feb 13 2016 *) PROG (PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 1]^n*[1; 0; 0; 0; 0; 0; 0; 0])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016 CROSSREFS For Lamé sequences of orders 1 through 9 see A000045, A000930, A017898-A017904. Sequence in context: A219955 A079064 A123176 * A005710 A367800 A291146 Adjacent sequences: A017899 A017900 A017901 * A017903 A017904 A017905 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 8 12:42 EDT 2024. Contains 375021 sequences. (Running on oeis4.)