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A002574 Restricted partitions.
(Formerly M1070 N0404)
8
0, 0, 1, 1, 2, 4, 7, 13, 24, 42, 76, 137, 245, 441, 792, 1420, 2550, 4576, 8209, 14732, 26433, 47424, 85092, 152670, 273914, 491453, 881744, 1581985, 2838333, 5092398, 9136528, 16392311, 29410243, 52766343, 94670652, 169853138, 304741614, 546751437, 980952673, 1759973660 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=3 and p(k) <= 2*p(k+1), see example.  [Joerg Arndt, Dec 18 2012]

REFERENCES

Even, Shimon; Lempel, Abraham; Generation and enumeration of all solutions of the characteristic sum condition. Information and Control 21 (1972), 476-482.

Minc, H.; A problem in partitions: Enumeration of elements of a given degree in the free commutative entropic cyclic groupoid. Proc. Edinburgh Math. Soc. (2) 11 (1958/1959), pp. 223-224.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

H. Minc, A problem in partitions: Enumeration of elements of a given degree in the free commutative entropic cyclic groupoid, Proc. Edinburgh Math. Soc. (2) 11 1958/1959 223-224.

EXAMPLE

From Joerg Arndt, Dec 18 2012: (Start)

There are a(8)=13 compositions 8=p(1)+p(2)+...+p(m) with p(1)=3 and p(k) <= 2*p(k+1):

[ 1]  [ 3 1 1 1 1 1 ]

[ 2]  [ 3 1 1 1 2 ]

[ 3]  [ 3 1 1 2 1 ]

[ 4]  [ 3 1 2 1 1 ]

[ 5]  [ 3 1 2 2 ]

[ 6]  [ 3 2 1 1 1 ]

[ 7]  [ 3 2 1 2 ]

[ 8]  [ 3 2 2 1 ]

[ 9]  [ 3 2 3 ]

[10]  [ 3 3 1 1 ]

[11]  [ 3 3 2 ]

[12]  [ 3 4 1 ]

[13]  [ 3 5 ]

(End)

MAPLE

v := proc(c, d) option remember; local i; if d < 0 or c < 0 then 0 elif d = c then 1 else add(v(i, d-c), i=1..2*c); fi; end; [ seq(v(3, n), n=1..50) ];

MATHEMATICA

v[c_, d_] := v[c, d] = If[d < 0 || c < 0, 0, If[d == c, 1, Sum[v[i, d-c], {i, 1, 2*c}]]]; a[n_] := v[3, n]; Table[a[n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Apr 05 2013, after Maple *)

CROSSREFS

Cf. A002572, A002573, A049284, A049285, A047913.

Sequence in context: A018182 A005595 A096236 * A069765 A090427 A006745

Adjacent sequences:  A002571 A002572 A002573 * A002575 A002576 A002577

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Michael Somos

STATUS

approved

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Last modified May 22 21:40 EDT 2017. Contains 286906 sequences.