A053732 Number of ways to partition {1,...,n} into arithmetic progressions of length >= 1.

1, 1, 2, 5, 13, 37, 111, 359, 1211, 4338, 16205, 63305, 254803, 1073370, 4638359, 20731961, 95072041, 449599410, 2170162939, 10782813595, 54579794359, 283240154578, 1497311544427, 8092773946020, 44438105067443, 249435020112771, 1420933555310524, 8249315265492112, 48599942367553271

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Example

a(4) gives the total number of partitions of {1,2,3,4} (Bell(4); see A000110) excluding the partitions {1,2,4}{3} and {1,3,4}{2}. Hence a(4) = 15 - 2 = 13.

Crossrefs

Cf. A000110, A072255.

Sequence in context: A149854 A151442 A263529 * A216617 A243412 A170941

Adjacent sequences: A053729 A053730 A053731 * A053733 A053734 A053735

Keyword

nonn,nice

Author

Marty Getz (ffmpg1(AT)uaf.edu) and Dixon Jones (fndjj(AT)uaf.edu), Feb 13 2000

Extensions

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), May 20 2001

a(15)-a(21) from Giovanni Resta, Feb 23 2009

a(0) prepended and a(22)-a(28) added by Max Alekseyev, Feb 11 2024

Status

approved