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A107345
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From the binary representation of n: binomial(number of zeros, number of blocks of contiguous zeros).
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3
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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; internal format)
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OFFSET
| 0,5
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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.
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LINKS
| Index entries for sequences related to binary expansion of n
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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, (rgwv(AT)rgwv.com), Apr 01 2008 *)
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CROSSREFS
| Cf. A007088, A107782, A136277.
Sequence in context: A091050 A005361 A008479 * A000688 A038538 A088529
Adjacent sequences: A107342 A107343 A107344 * A107346 A107347 A107348
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 23 2005
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