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A017900
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Expansion of 1/(1 -x^6 -x^7 -x^8 - ...).
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2
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1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 21, 27, 34, 43, 55, 71, 92, 119, 153, 196, 251, 322, 414, 533, 686, 882, 1133, 1455, 1869, 2402, 3088, 3970, 5103, 6558, 8427, 10829, 13917, 17887, 22990
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| A Lamé sequence of higher order.
Number of compositions of n into parts >=6. [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.: 1/(1-sum(k>=6,x^k)).
G.f.: (1-x)/(1-x-x^6). [From Alois P. Heinz, Aug 04 2008]
For positive integers n and k such that k <= n <= 6*k, and 5 devides n-k, define c(n,k) = binomial(k,(n-k)/5), and c(n,k )= 0, otherwise. Then, for n>=1, a(n+6) = 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(6, (i, j)-> `if` (i=j-1, 1, `if` (j=1, [1, 0$4, 1][i], 0)))^n)[6, 6]: seq (a(n), n=0..50); [From Alois P. Heinz, Aug 04 2008]
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MATHEMATICA
| f[n_] := If[n < 1, 1, Sum[ Binomial[ n - 5 k - 5, k], {k, 0, (n - 5)/6}]]; Array[f, 49, 0] (* Adi Dani, Robert G. Wilson, Jul 04 2011 *)
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CROSSREFS
| For Lamé sequences of orders 1 through 9 see A000045, A000930, A017898-A017904.
Sequence in context: A126327 A193286 A098132 * A005708 A085793 A143286
Adjacent sequences: A017897 A017898 A017899 * A017901 A017902 A017903
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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