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A108538 Column 10 of array illustrated in A089574 and related to A034261. 8
1, 64, 731, 4553, 20155, 71272, 214653, 572743, 1389702, 3122752, 6585183, 13162741, 25131718, 46115029, 81722067, 140429357, 234772177, 382932581, 610826859, 954815625, 1465182669, 2210554686, 3283463257, 4807283267, 6944818576, 9908846494, 13974977743, 19497238421, 26926835328 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A000330 (column 2), A086602 (column 3), A089574 (column 4), A107600 (column 5), A107601 (column 6), A109125 (column 7), A109126 (column 8), A109820 (column 9), A108538 (column 10), A109821 (column 11), A110553 (column 12), A110624 (column 13)

Sequence in context: A056573 A321817 A231305 * A195593 A221753 A055867

Adjacent sequences:  A108535 A108536 A108537 * A108539 A108540 A108541

KEYWORD

easy,nonn

AUTHOR

Alford Arnold, Jul 05 2005

EXTENSIONS

Extended by R. J. Mathar, Aug 28 2018

STATUS

approved

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Last modified June 22 14:35 EDT 2021. Contains 345380 sequences. (Running on oeis4.)