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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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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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
| T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
| 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
| Row 4 is 1 4 6 4 1 with 3 even entries so a(4)=3.
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MATHEMATICA
| Table[n + 1 - Sum[ Mod[ Binomial[n, k], 2], {k, 0, n} ], {n, 0, 100} ]
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PROG
| (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
| Cf. A007318, A001316, A000120, A000225.
Sequence in context: A103491 A089306 A086099 * A166592 A103497 A191390
Adjacent sequences: A048964 A048965 A048966 * A048968 A048969 A048970
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KEYWORD
| easy,nonn
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AUTHOR
| Brian L. Galebach (sequence(AT)ProbabilitySports.com)
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