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A017903
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Expansion of 1/(1 - x^9 - x^10 - ...).
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,19
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COMMENTS
| A Lam{\'e} sequence of higher order.
For n>=1, a(n) = number of compositions of n in which each part is >=9. [From Milan R. Janjic (agnus(AT)blic.net), Jun 28 2010]
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REFERENCES
| J. Hermes, Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden, Math. Ann., 45 (1894), 371-380.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1)
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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 devides 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
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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
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CROSSREFS
| For Lam{\'e} sequences of orders 1 through 9 see A000045, A000930, A017898-A017904.
Sequence in context: A102576 A101170 A130224 * A005711 A059765 A180479
Adjacent sequences: A017900 A017901 A017902 * A017904 A017905 A017906
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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