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A239471 Number of 5-separable partitions of n; see Comments. 4
0, 0, 0, 0, 0, 1, 2, 2, 3, 2, 4, 5, 7, 8, 9, 11, 13, 16, 20, 23, 27, 31, 37, 43, 52, 59, 70, 80, 93, 108, 126, 144, 167, 191, 221, 253, 292, 332, 382, 435, 498, 567, 649, 736, 839, 951, 1082, 1226, 1393, 1573, 1784, 2013, 2277, 2568, 2902, 3266, 3683, 4141 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Suppose that p is a partition of n into 2 or more parts and that h is a part of p.  Then p is (h,0)-separable if there is an ordering x, h, x, h, ..., h, x of the parts of p, where each x represents any part of p except h.  Here, the number of h's on the ends of the ordering is 0.  Similarly, p is (h,1)-separable if there is an ordering x, h, x, h, ... , x, h, where the number of h's on the ends is 1; next, p is (h,2)-separable if there is an ordering h, x, h, ... , x, h.  Finally, p is h-separable if it is (h,i)-separable for i = 0,1,2.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

(5,0)-separable partitions of 7:  151

(5,1)-separable partitions of 7:  52

(5,2)-separable partitions of 7:  (none)

5-separable partitions of 7:  151, 52, so that a(7) = 2.

MATHEMATICA

z = 55; t1 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 1] <= Length[p] + 1], {n, 1, z}] (* A239467 *)

t2 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 2] <= Length[p] + 1], {n, 1, z}] (* A239468 *)

t3 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 3] <= Length[p] + 1], {n, 1, z}] (* A239469 *)

t4 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 4] <= Length[p] + 1], {n, 1, z}] (* A239470 *)

t5 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 5] <= Length[p] + 1], {n, 1, z}] (* A239472 *)

CROSSREFS

Cf. A239467, A239468, A239469, A239470.

Sequence in context: A319706 A305894 A305811 * A241509 A268327 A053023

Adjacent sequences:  A239468 A239469 A239470 * A239472 A239473 A239474

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 20 2014

STATUS

approved

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Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)