login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049285 Restricted partitions. 6
0, 0, 0, 0, 1, 1, 2, 4, 7, 13, 24, 43, 78, 141, 253, 455, 818, 1468, 2637, 4734, 8495, 15247, 27361, 49094, 88093, 158063, 283599, 508840, 912956, 1638003, 2938861, 5272795, 9460227, 16973125, 30452380, 54636174, 98025512, 175872397, 315541228, 566127763 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=5 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 & 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(10)=13 compositions 10=p(1)+p(2)+...+p(m) with p(1)=5 and p(k) <= 2*p(k+1):

[ 1]  [ 5 1 1 1 1 1 ]

[ 2]  [ 5 1 1 1 2 ]

[ 3]  [ 5 1 1 2 1 ]

[ 4]  [ 5 1 2 1 1 ]

[ 5]  [ 5 1 2 2 ]

[ 6]  [ 5 2 1 1 1 ]

[ 7]  [ 5 2 1 2 ]

[ 8]  [ 5 2 2 1 ]

[ 9]  [ 5 2 3 ]

[10]  [ 5 3 1 1 ]

[11]  [ 5 3 2 ]

[12]  [ 5 4 1 ]

[13]  [ 5 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(5, 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[5, n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Jan 10 2014, translated from Maple *)

CROSSREFS

Cf. A002572, A002573, A049284, A002574.

Sequence in context: A090427 A006745 A049284 * A002843 A128742 A107281

Adjacent sequences:  A049282 A049283 A049284 * A049286 A049287 A049288

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Michael Somos

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

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