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A079971 Number of compositions (ordered partitions) of n into parts 1, 2, and 5. 3
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; text; internal format)
OFFSET

0,3

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}.

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.

LINKS

Table of n, a(n) for n=0..36.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,1).

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} C(j,n-5*k+4*j)*C(k,j). - Vladimir Kruchinin, Dec 15 2011

With offset 1, the INVERT transform of (1 + x + x^4). - Gary W. Adamson, Apr 01 2017

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); # Alois P. Heinz, Oct 07 2008

MATHEMATICA

LinearRecurrence[{1, 1, 0, 0, 1}, {1, 1, 2, 3, 5}, 40] (* Jean-Fran├žois Alcover, Nov 11 2015 *)

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); /* Vladimir Kruchinin, Dec 15 2011 */

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

KEYWORD

nonn

AUTHOR

Vladimir Baltic, Feb 17 2003

EXTENSIONS

Entry revised by N. J. A. Sloane, Feb 23 2006

STATUS

approved

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Last modified April 3 04:21 EDT 2020. Contains 333195 sequences. (Running on oeis4.)