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A017904
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Expansion of 1/(1 - x^10 - x^11 - ...).
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10
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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; internal format)
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OFFSET
| 0,21
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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 >=10. [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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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 devides 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
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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(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
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CROSSREFS
| For Lam{\'e} sequences of orders 1 through 9 see A000045, A000930, A017898-A017903, this one.
Sequence in context: A101373 A107062 A178538 * A143290 A044961 A044823
Adjacent sequences: A017901 A017902 A017903 * A017905 A017906 A017907
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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