OFFSET
0,2
COMMENTS
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) p. 831. 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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
G.f. 1+64*x -x^2*(-731 +4219*x -13765*x^2 +30910*x^3 -49804*x^4 +58458*x^5 -50237*x^6 +31394*x^7 -13931*x^8 +4171*x^9 -757*x^10 +63*x^11)/(x-1)^12 . - R. J. Mathar, Aug 28 2018
EXAMPLE
a(1) = 1 because the only associated partition 4444 for n = 16 cannot be permuted.
a(2) = 64 because the associated partitions can be permuted in 3 + 4 + 12 + 9 + 20 + 10 + 6 ways when n = 17.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Alford Arnold, Jul 05 2005
EXTENSIONS
Extended by R. J. Mathar, Aug 28 2018
STATUS
approved