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A239470 Number of 4-separable partitions of n; see Comments. 5
0, 0, 0, 0, 1, 2, 2, 2, 3, 5, 6, 7, 8, 11, 13, 17, 19, 23, 27, 34, 40, 47, 55, 66, 77, 92, 106, 125, 145, 171, 198, 231, 266, 310, 358, 416, 477, 552, 633, 731, 838, 963, 1100, 1263, 1442, 1651, 1880, 2147, 2442, 2785, 3163, 3597, 4078, 4631, 5244, 5946 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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..56.

EXAMPLE

(4,0)-separable partitions of 7:  241

(4,1)-separable partitions of 7:  43

(4,2)-separable partitions of 7:  (none)

4-separable partitions of 7:  241, 43, 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, A239471.

Sequence in context: A077018 A007918 A278167 * A320786 A126111 A296103

Adjacent sequences:  A239467 A239468 A239469 * A239471 A239472 A239473

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 20 2014

STATUS

approved

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Last modified October 15 18:26 EDT 2019. Contains 328037 sequences. (Running on oeis4.)