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 A107345 From the binary representation of n: binomial(number of zeros, number of blocks of contiguous zeros). 4
 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 3, 3, 2, 3, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 5, 4, 6, 3, 6, 3, 3, 2, 6, 3, 1, 1, 3, 1, 1, 1, 4, 3, 3, 2, 3, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 6, 5, 10, 4, 10, 6, 6, 3, 10, 6, 4, 3, 6, 3, 3, 2, 10, 6, 4, 3, 4, 1, 1, 1, 6, 3, 1, 1, 3, 1, 1, 1, 5, 4, 6, 3, 6, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(n) = binomial(A023416(n), A087116(n)); a(A003754(n)) = 1. First occurrence of k: 1, 4, 8, 16, 32, 34, 128, 256, 512, 66, 2048, 4096, 8192, 16384, 130, 65536, 131072, 262144, 524288, 266, 258, ..., . k must occur by 2^k. - Robert G. Wilson v Record values: 1, 4, 8, 16, 32, 34, 66, 130, 258, 514, 522, 1026, 1034, 2058, 4106, 4138, 8202, 8234, 16394, 16426, 32810, 65578, 65706, 131114, 131242, 262186, 262314, 524458, 1048746, 1049258, 2097322, 2097834, 4194474, 4194986, 8389290, 8391338, ..., . - Robert G. Wilson v LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 MATHEMATICA f[n_] := Block[{id = IntegerDigits[n, 2]}, Binomial[ Count[id, 0], Floor[(Length@ Split@ id + 1)/2]]]; Table[f@n, {n, 0, 102}] (* Robert G. Wilson v, Apr 01 2008 *) PROG (Haskell) a107345 n = a007318' (a023416 n) (a087116 n) -- Reinhard Zumkeller, Mar 31 2015 CROSSREFS Cf. A007088, A107782, A136277. Cf. A007318, A023416, A087116. Sequence in context: A008479 A331178 A227350 * A336736 A000688 A295879 Adjacent sequences:  A107342 A107343 A107344 * A107346 A107347 A107348 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 23 2005 STATUS approved

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Last modified September 21 02:46 EDT 2020. Contains 337266 sequences. (Running on oeis4.)