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A049284 Restricted partitions. 6
0, 0, 0, 1, 1, 2, 4, 7, 13, 24, 43, 78, 140, 251, 452, 812, 1457, 2617, 4697, 8428, 15126, 27142, 48700, 87384, 156787, 281307, 504723, 905562, 1624731, 2915039, 5230040, 9383505, 16835453, 30205347, 54192931, 97230224, 174445475, 312981054, 561534340, 1007475560 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=4 and p(k) <= 2*p(k+1), see example.  [Joerg Arndt, Dec 18 2012]

REFERENCES

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 223-224.

LINKS

Table of n, a(n) for n=1..40.

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

EXAMPLE

From Joerg Arndt, Dec 18 2012: (Start)

There are a(9)=13 compositions 9=p(1)+p(2)+...+p(m) with p(1)=4 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(4, 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}]]]; Table[v[4, n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Jan 10 2014, translated from Maple *)

CROSSREFS

Cf. A002572, A002573, A002574, A049285.

Sequence in context: A069765 A090427 A006745 * A049285 A002843 A128742

Adjacent sequences:  A049281 A049282 A049283 * A049285 A049286 A049287

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Michael Somos

STATUS

approved

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Last modified March 27 22:02 EDT 2017. Contains 284182 sequences.