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 A017903 Expansion of 1/(1 - x^9 - x^10 - ...). 6
 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 19, 24, 30, 37, 45, 54, 64, 76, 91, 110, 134, 164, 201, 246, 300, 364, 440, 531, 641, 775, 939, 1140, 1386, 1686, 2050, 2490, 3021, 3662, 4437, 5376, 6516, 7902, 9588 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,19 COMMENTS A Lamé sequence of higher order. a(n) = number of compositions of n in which each part is >=9. - Milan Janjic, Jun 28 2010 a(n+9) equals the number of n-length binary words such that 0 appears only in a run which length is a multiple of 9. - 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 (1,0,0,0,0,0,0,0,1) FORMULA G.f.: (x-1)/(x-1+x^9). - Alois P. Heinz, Aug 04 2008 For positive integers n and k such that k <= n <= 9*k, and 8 divides n-k, define c(n,k) = binomial(k,(n-k)/8), and c(n,k) = 0, otherwise. Then, for n>= 1, a(n+9) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011 a(n) = A005711(n-10) for n > 9. - Alois P. Heinz, May 21 2018 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(9, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0\$7, 1][i] else 0 fi)^n)[9, 9]: seq(a(n), n=0..55); # Alois P. Heinz, Aug 04 2008 MATHEMATICA CoefficientList[(1-x)/(1-x-x^9) + O[x]^70, x] (* Jean-François Alcover, Jun 08 2015 *) PROG (PARI) Vec((x-1)/(x-1+x^9)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012 CROSSREFS For Lamé sequences of orders 1 through 9 see A000045, A000930, A017898-A017904. Cf. A005711. Sequence in context: A246084 A260768 A130224 * A005711 A322856 A280863 Adjacent sequences: A017900 A017901 A017902 * A017904 A017905 A017906 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)