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A017902
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Expansion of 1/(1 - x^8 - x^9 - ...).
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2
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1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 64, 78, 96, 119, 148, 184, 228, 281, 345, 423, 519, 638, 786, 970, 1198, 1479, 1824, 2247, 2766, 3404, 4190, 5160
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,17
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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 >=8. [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^8). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008]
For positive integers n and k such that k <= n <= 8*k, and 7 devides n-k, define c(n,k) = binomial(k,(n-k)/7), and c(n,k) = 0, otherwise. Then, for n>=1, a(n+8) = 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
(Maple) a := n -> (Matrix(8, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0$6, 1][i] else 0 fi)^n)[8, 8] ; seq (a(n), n=0..53); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 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: A082324 A079064 A123176 * A005710 A023358 A061379
Adjacent sequences: A017899 A017900 A017901 * A017903 A017904 A017905
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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