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A079272
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a(n)=[(2n+1)*3^n - 1]/2.
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3
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4, 22, 94, 364, 1336, 4738, 16402, 55768, 186988, 620014, 2037190, 6643012, 21523360, 69353050, 222408058, 710270896, 2259952852, 7167279046, 22664098606, 71479080220, 224897593864, 706073841202, 2212364702434
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sequence corresponds to the maximum chain length of a variant of the classical puzzle whereby, under agreed terms, a ringed golden chain asset of a(n) links, when judiciously fragmented into n opened links(through n cuts) and n pieces of lengths (2n+1), (2n+1)*3, (2n+1)*3^2, ..., (2n+1)*3^(n-1), may be used to sequentially settle for payment equivalent up to a(n)-link cost, a link-cost at a time, with swapping allowed with identical fragments owned by the creditor.
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EXAMPLE
| For instance the 4 fragmented chains of original length a(4)=364 into
.1.+..9..+.1
.+.........+
243.......27
.+.........+
.1.+..81.+.1
when swapped with identical fragments owned by the creditor, enable the sequential payment, a link-cost at a time, for an expense up to 364 link-costs.
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MAPLE
| a:=n->sum (3^j*n^binomial(j, n), j=0..n): seq(a(n), n=1..23); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 18 2009]
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CROSSREFS
| Cf. A014915, A064017, A027261.
Sequence in context: A027074 A036922 A036926 * A197667 A007901 A088581
Adjacent sequences: A079269 A079270 A079271 * A079273 A079274 A079275
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Feb 06 2003
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EXTENSIONS
| More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Jun 20 2003
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