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

0,5

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

Index entries for sequences related to binary expansion of n

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 * A358780 A336736 A000688

Adjacent sequences: A107342 A107343 A107344 * A107346 A107347 A107348

Keyword

nonn

Author

Reinhard Zumkeller, May 23 2005

Status

approved