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A017904 Expansion of 1/(1 - x^10 - x^11 - ...). 11
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 20, 25, 31, 38, 46, 55, 65, 76, 89, 105, 125, 150, 181, 219, 265, 320, 385, 461, 550, 655, 780, 930, 1111, 1330, 1595, 1915, 2300, 2761, 3311, 3966, 4746, 5676 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,21

COMMENTS

A Lamé sequence of higher order.

a(n) = number of compositions of n in which each part is >=10. - Milan Janjic, Jun 28 2010

a(n+19) equals the number of binary words of length n having at least 9 zeros between every two successive ones. - Milan Janjic, Feb 09 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

J. Hermes, Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden, Math. Ann., 45 (1894), 371-380.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 1).

FORMULA

G.f.: (x-1)/(x-1+x^10). - Alois P. Heinz, Aug 04 2008

For positive integers n and k such that k <= n <= 10*k, and 9 divides n-k, define c(n,k) = binomial(k,(n-k)/9), and c(n,k) = 0, otherwise. Then, for n>= 1, a(n+10) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011

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(10, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0$8, 1][i] else 0 fi)^n)[10, 10]: seq(a(n), n=0..80); # Alois P. Heinz, Aug 04 2008

MATHEMATICA

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)

PROG

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]^n)[1, 1] \\ Charles R Greathouse IV, Oct 03 2016

CROSSREFS

For Lamé sequences of orders 1 through 9 see A000045, A000930, A017898-A017903, and this one.

Sequence in context: A101373 A107062 A178538 * A143290 A272038 A044961

Adjacent sequences:  A017901 A017902 A017903 * A017905 A017906 A017907

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)