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A087079
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Number of dismal partitions of n: number of ways of writing n as a dismal sum of distinct terms, ignoring order.
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2
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1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 5, 22, 92, 376, 1520, 6112, 24512, 98176, 392960, 2, 22, 200, 1696, 13952, 113152, 911360, 7315456, 58621952, 469368832, 4, 92, 1696, 28928, 477184, 7749632, 124911616, 2005925888, 32153534464, 514926313472, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Without the condition that the numbers are distinct the answers are infinite because 1+1+1+...+1 = 1 in dismal arithmetic - see A087061.
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LINKS
| D Applegate and N. J. A. Sloane, Table of n, a(n) for n = 0..2000
D. Applegate, C program for dismal arithmetic and number theory
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic
Index entries for sequences related to dismal arithmetic
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FORMULA
| For 1 <= a < 10 and 0 <= b < 10, a(10a+b) = 2^(ab+a+b-1)+(2^a-1)(2^b-1)2^(ab-1). - David Wasserman (wasserma(AT)spawar.navy.mil), Apr 14 2005
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EXAMPLE
| a(5) = 16: we can write 5 = 5 + any subset of {4, 3, 2, 1} (16 ways).
a(12) = 22: we can write 12 = 12 + any subset of {11, 10, 2, 1} (16 ways), 12 = 2 + 11 + 10 = 2 + 11 = 2 + 10 and those three with 1 added (6 ways).
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CROSSREFS
| Cf. A010036.
The subsequence a(n) where n = 111..11 is A003465. - N. J. A. Sloane, may 21 2011.
Sequence in context: A172317 A079262 A194631 * A009694 A097000 A054046
Adjacent sequences: A087076 A087077 A087078 * A087080 A087081 A087082
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KEYWORD
| nonn
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AUTHOR
| Marc LeBrun (mlb(AT)well.com), Oct 09 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Apr 14 2005
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