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A017901
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Expansion of 1/(1 - x^7 - x^8 - ...).
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2
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1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 28, 35, 43, 53, 66, 83, 105, 133, 168, 211, 264, 330, 413, 518, 651, 819, 1030, 1294, 1624, 2037, 2555, 3206, 4025, 5055, 6349, 7973
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,15
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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 >=7. [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^7). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008]
For positive integers n and k such that k <= n <= 7*k, and 6 devides n-k, define c(n,k) = binomial(k,(n-k)/6), and c(n,k) = 0, otherwise. Then, for n>=1, a(n+7) = 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(7, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0$5, 1][i] else 0 fi)^n)[7, 7]; seq (a(n), n=0..50); [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, A017899, A017900, A017901, A017902, A017903, A017904.
Sequence in context: A061920 A062010 A071218 * A005709 A101917 A127273
Adjacent sequences: A017898 A017899 A017900 * A017902 A017903 A017904
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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