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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235130 Triangular array:  t(n,k) = number of partitions of n that include a partition of k. 4
1, 1, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 8, 6, 7, 7, 11, 11, 11, 11, 11, 10, 11, 15, 15, 17, 15, 14, 13, 15, 15, 22, 22, 23, 23, 21, 22, 19, 20, 22, 30, 30, 33, 30, 33, 25, 29, 25, 29, 30, 42, 42, 45, 44, 43, 41, 42, 36, 36, 39, 42, 56, 56, 62, 58, 60 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..300

FORMULA

t(n,1) = A000041(n-1) for n>=0; t(n,n) = A000041(n) for n >= 1.

EXAMPLE

The eleven partitions of 6 include the following six, written as multisets:  {1,1,1,1,1,1}, {1,1,1,1,2}, {1,1,2,2}, {1,1,1,3}, {1,2,3}, {3,3}; each has a sub-multiset of which the sum of terms is 3.  None of the remaining five partitions of 6 has this property, so t(6,3) = 6.  First 7 rows:

1

1 ... 2

2 ... 2 ... 3

3 ... 3 ... 3 ... 5

5 ... 5 ... 5 ... 5 ... 7

7 ... 8 ... 6 ... 7 ... 7 ... 11

11 .. 11 .. 11 .. 11 .. 10 .. 11 .. 15

MATHEMATICA

p[n_] := p[n] = IntegerPartitions[n]; t = Table[Length[Cases[p[n], Apply[Alternatives, Map[Flatten[{___, #, ___}] &, p[k]]]]], {n, 15}, {k, n}]; u = Flatten[t] (* 235130 *)

TableForm[t] (* Peter J. C. Moses, Jan 04 2014 *)

CROSSREFS

Cf. A000041.

Sequence in context: A157873 A022870 A237050 * A131410 A202453 A259529

Adjacent sequences:  A235127 A235128 A235129 * A235131 A235132 A235133

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 03 2014

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 28 19:06 EDT 2017. Contains 284246 sequences.