A107345 From the binary representation of n: binomial(number of zeros, number of blocks of contiguous zeros).

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

Offset: 0

Author

Reinhard Zumkeller, May 23 2005

Keywords

• nonn

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
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A007088, A107782, A136277.

Cf. A007318, A023416, A087116.

Programs

Haskell

a107345 n = a007318' (a023416 n) (a087116 n)
-- Reinhard Zumkeller, Mar 31 2015

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 *)