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Search: id:A017903
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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; listen)
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OFFSET
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0,19
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COMMENT
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A Lam{\'e} sequence of higher order.
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REFERENCES
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J. Hermes, Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden, Math. Ann., 45 (1894), 371-380.
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FORMULA
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G.f.: (x-1)/(x-1+x^9). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008]
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MAPLE
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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(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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008]
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CROSSREFS
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For Lam{\'e} sequences of orders 1 through 9 see A000045, A000930, A017898-A017904.
Sequence in context: A102576 A101170 A130224 this_sequence A005711 A059765 A143289
Adjacent sequences: A017900 A017901 A017902 this_sequence A017904 A017905 A017906
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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