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 A048967 Number of even entries in row n of Pascal's triangle (A007318). 17
 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; text; internal format)
 OFFSET 0,5 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 Also number of zeros in n-th row of Sierpiński's triangle (cf. A047999): a(n) = A023416(A001317(n)). - Reinhard Zumkeller, Nov 24 2012 a(n) = row sums in A219463 = A000120(A219843(n)). - Reinhard Zumkeller, Nov 30 2012 A249304(n+1) = a(n+1) + a(n). - Reinhard Zumkeller, Nov 14 2014 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe) 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, Oct 07 2003 G.f.: 1/(1 - x)^2 - Product_{k>=0} (1 + 2*x^(2^k)). - Ilya Gutkovskiy, Jul 19 2019 EXAMPLE Row 4 is 1 4 6 4 1 with 3 even entries so a(4)=3. MATHEMATICA Table[n + 1 - Sum[ Mod[ Binomial[n, k], 2], {k, 0, n} ], {n, 0, 100} ] PROG (PARI) a(n)=if(n<1, 0, if(n%2==0, a(n/2)+n/2, 2*a((n-1)/2))) (Haskell) import Data.List (transpose) a048967 n = a048967_list !! n a048967_list = 0 : xs where    xs = 0 : concat (transpose [zipWith (+) [1..] xs, map (* 2) xs]) -- Reinhard Zumkeller, Nov 14 2014, Nov 24 2012 CROSSREFS Cf. A007318, A001316, A000120, A000225, A038573. Cf. A249304. Sequence in context: A089306 A244996 A086099 * A324182 A166592 A103497 Adjacent sequences:  A048964 A048965 A048966 * A048968 A048969 A048970 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified August 3 14:45 EDT 2020. Contains 336198 sequences. (Running on oeis4.)