

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
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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 nlength 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), 371380.
Augustine O. Munagi, Integer Compositions and HigherOrder 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.: (x1)/(x1+x^9).  Alois P. Heinz, Aug 04 2008
For positive integers n and k such that k <= n <= 9*k, and 8 divides nk, define c(n,k) = binomial(k,(nk)/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(n10) 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[i1]+t1[i1r]]; od: t1; end; # set r = order
a:= n> (Matrix(9, (i, j)> if (i=j1) 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[(1x)/(1xx^9) + O[x]^70, x] (* JeanFrançois Alcover, Jun 08 2015 *)


PROG

(PARI) Vec((x1)/(x1+x^9)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012


CROSSREFS

For Lamé sequences of orders 1 through 9 see A000045, A000930, A017898A017904.
Cf. A005711.
Sequence in context: A246084 A260768 A130224 * A005711 A322856 A280863
Adjacent sequences: A017900 A017901 A017902 * A017904 A017905 A017906


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



