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Search: id:A087079
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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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1
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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; listen)
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OFFSET
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0,3
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COMMENT
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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
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D. Applegate, C program for dismal arithmetic and number theory
Index entries for sequences related to dismal arithmetic
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FORMULA
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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
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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
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Cf. A010036.
Sequence in context: A008860 A145114 A079262 this_sequence A009694 A097000 A054046
Adjacent sequences: A087076 A087077 A087078 this_sequence A087080 A087081 A087082
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KEYWORD
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nonn
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Oct 09 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Apr 14 2005
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