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A079971
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Number of compositions (ordered partitions) of n into elements of the set {1,2,5}.
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1
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1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 128, 218, 372, 634, 1081, 1843, 3142, 5357, 9133, 15571, 26547, 45260, 77164, 131557, 224292, 382396, 651948, 1111508, 1895013, 3230813, 5508222, 9390983, 16010713, 27296709, 46538235, 79343166, 135272384
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of ways of ordered sequences of nickels, dimes and quarters that add to 5n cents.
Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=4, I={2,3}.
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REFERENCES
| D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.
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FORMULA
| Recurrence: a(n) = a(n-1)+a(n-2)+a(n-5). G.f.: 1/(1-x-x^2-x^5).
a(n)=sum(k=0..n, sum(j=floor((5*k-n)/4)..k, binomial(j,n-5*k+4*j)*binomial(k,j))). [From Vladimir Kruchinin, Dec 15 2011]
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MAPLE
| a:= n-> (Matrix(5, (i, j)-> if i+1=j or j=1 and member (i, [1, 2, 5]) then 1 else 0 fi)^n)[1, 1]: seq (a(n), n=0..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 07 2008]
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PROG
| (Maxima)
a(n):=sum(sum(binomial(j, n-5*k+4*j)*binomial(k, j), j, floor((5*k-n)/4), k), k, 0, n); [From Vladimir Kruchinin, Dec 15 2011]
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CROSSREFS
| Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A073031.
Sequence in context: A034063 A034073 A114623 * A073031 A114138 A114140
Adjacent sequences: A079968 A079969 A079970 * A079972 A079973 A079974
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KEYWORD
| nonn
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AUTHOR
| Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Feb 17 2003
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Feb 23, 2006
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