0,2

A109820 can be decomposed into 30 sequences. These 30 associated sequences can be inferred from the 30 ways of partitioning the number nine: 9 81 72 63 54 ... the complete listing is available in the Handbook of Mathematical Functions (1964) p831. Consider, for example, the three ways of partitioning the number three: 3, 21 and 111; prepend each partition then add one to each value - yielding 44, 332 and 2222. These "associated" partitions are then used to derive the associated sequences. 44 => A000330, 332 => A006011 and 2222 => A034263. Summing these three sequences yields A089574.

a(1) = 1 because the only associated partition 4444 for n = 16 can not be permuted.

a(2) = 64 because the associated partitions can be permuted in 3 + 4 + 12 + 9 + 20 + 10 + 6 ways when n = 17.

Sequence in context: A092758 A030516 A056573 this_sequence A055867 A027003 A000818

Adjacent sequences: A108535 A108536 A108537 this_sequence A108539 A108540 A108541

easy,more,nonn

Alford Arnold (Alford1940(AT)aol.com), Jul 05 2005