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A052934
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Expansion of (1-x)/(1-6*x).
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13
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1, 5, 30, 180, 1080, 6480, 38880, 233280, 1399680, 8398080, 50388480, 302330880, 1813985280, 10883911680, 65303470080, 391820820480, 2350924922880, 14105549537280, 84633297223680, 507799783342080
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OFFSET
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0,2
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COMMENTS
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With formula a(n) = (5*6^n + 0^n)/6, this is the binomial transform of A083425. - Paul Barry, Apr 30 2003
For n>=1, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6} we have f(x) != y. - Aleksandar M. Janjic and Milan Janjic, Mar 27 2007
a(n) = (n+1) terms in the sequence (1, 4, 5, 5, 5, ...) dot (n+1) terms in the sequence (1, 1, 5, 30, 180, 1080, ...). Example: a(4) = (1, 4, 5, 5, 5) dot (1, 1, 5, 30, 180) = (1 + 4 + 25 + 150 + 900), where (1, 4, 25, 150, ...) = first differences of current sequence. - Gary W. Adamson, Aug 03 2010
a(n) is the number of compositions of n when there are 5 types of each natural number. - Milan Janjic, Aug 13 2010
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LINKS
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FORMULA
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a(n) = 6*a(n-1), n>=2.
G.f.: (1-x)/(1-6*x).
G.f.: 1/(1 - 5*Sum_{k>=1} x^k).
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MAPLE
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spec := [S, {S=Sequence(Prod(Sequence(Z), Union(Z, Z, Z, Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
seq(`if`(n=0, 1, 5*6^(n-1)), n=0..30); # G. C. Greubel, Oct 18 2019
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MATHEMATICA
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PROG
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(PARI) vector(31, n, if(n==1, 1, 5*6^(n-2))) \\ G. C. Greubel, Oct 18 2019
(Magma) [1] cat [5*6^(n-1): n in [1..30]]; // G. C. Greubel, Oct 18 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 22); Coefficients(R!( (1-x)/(1-6*x))); // Marius A. Burtea, Oct 18 2019
(Sage) [1]+[5*6^(n-1) for n in (1..30)] # G. C. Greubel, Oct 18 2019
(GAP) Concatenation([1], List([1..30], n-> 5*6^(n-1) )); # G. C. Greubel, Oct 18 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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