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Search: id:A048967
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| A048967 |
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Number of even entries in row n of Pascal's triangle (A007318). |
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+0
9
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| 0, 0, 1, 0, 3, 2, 3, 0, 7, 6, 7, 4, 9, 6, 7, 0, 15, 14, 15, 12, 17, 14, 15, 8, 21, 18, 19, 12, 21, 14, 15, 0, 31, 30, 31, 28, 33, 30, 31, 24, 37, 34, 35, 28, 37, 30, 31, 16, 45, 42, 43, 36, 45, 38, 39, 24, 49, 42, 43, 28, 45, 30, 31, 0, 63, 62, 63, 60, 65, 62, 63, 56, 69, 66, 67
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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In rows 2^k - 1 all entries are odd.
a(n) = 0 (all the entries in the row are odd) iff n = 2^m - 1 for some m >= 0 and then n belongs to sequence A000225. - Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
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a(n) = n+1 - A001316(n) = n+1 - 2^A000120(n) = n+1 - Sum_{k=0..n} (C(n, k) mod 2) = Sum_{ k=0..n} ((1 - C(n, k)) mod 2)
a(2n) = a(n) + n, a(2n+1) = 2a(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 07 2003
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EXAMPLE
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Row 4 is 1 4 6 4 1 with 3 even entries so a(4)=3.
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MATHEMATICA
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Table[n + 1 - Sum[ Mod[ Binomial[n, k], 2], {k, 0, n} ], {n, 0, 100} ]
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PROGRAM
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(PARI) a(n)=if(n<1, 0, if(n%2==0, a(n/2)+n/2, 2*a((n-1)/2)))
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CROSSREFS
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Cf. A007318, A001316, A000120, A000225.
Sequence in context: A103491 A089306 A086099 this_sequence A103497 A085747 A106693
Adjacent sequences: A048964 A048965 A048966 this_sequence A048968 A048969 A048970
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KEYWORD
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easy,nonn
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AUTHOR
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Brian L. Galebach (sequence(AT)ProbabilitySports.com)
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