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Search: id:A089178
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| A089178 |
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Triangle T(n,k) (n >= 0, 0 <= k <= 1+log_2(floor(n+1)) read by rows: row 0 = {1}, row 1 = {1 1}; for n >=2, row n = row n-1 + (row floor((n-1)/2) shifted one place right). |
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+0
2
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| 1, 1, 1, 1, 2, 1, 3, 1, 1, 4, 2, 1, 5, 4, 1, 6, 6, 1, 7, 9, 1, 1, 8, 12, 2, 1, 9, 16, 4, 1, 10, 20, 6, 1, 11, 25, 10, 1, 12, 30, 14, 1, 13, 36, 20, 1, 14, 42, 26, 1, 15, 49, 35, 1, 1, 16, 56, 44, 2, 1, 17, 64, 56, 4, 1, 18, 72, 68, 6, 1, 19, 81, 84, 10, 1, 20, 90, 100, 14, 1, 21, 100, 120, 20
(list; graph; listen)
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OFFSET
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0,5
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LINKS
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N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
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FORMULA
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G.f.: (1/(1-x))*(1+Sum(y^(k+1)*x^(2^(k+1)-1)/Product(1-x^(2^j), j=0..k), k=0..infinity)).
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EXAMPLE
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Triangle begins:
1
1 1
1 2
1 3 1
1 4 2
1 5 4
1 6 6
1 7 9 1
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CROSSREFS
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Also obtained by dividing rows of A089177 by "1 1".
Row sums give A033485.
Sequence in context: A088425 A010766 A135841 this_sequence A116599 A138121 A138151
Adjacent sequences: A089175 A089176 A089177 this_sequence A089179 A089180 A089181
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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njas, Dec 08 2003
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 10 2003
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