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Search: id:A136277
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| A136277 |
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From the binary representation of n: binomial(number of ones, number of blocks of contiguous ones). |
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+0
2
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| 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 3, 2, 3, 3, 4, 1, 1, 1, 3, 1, 1, 3, 6, 2, 3, 3, 6, 3, 6, 4, 5, 1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 4, 3, 4, 6, 10, 2, 3, 3, 6, 3, 4, 6, 10, 3, 6, 6, 10, 4, 10, 5, 6, 1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 4, 3, 4, 6, 10, 1, 1, 1, 4, 1, 1, 4, 10, 3, 4, 4, 10, 6, 10, 10, 15, 2, 3, 3, 6
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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First occurrence of k: 1, 3, 7, 15, 31, 23, 127, 255, 511, 47, 2047, 4095, 8191, 16383, 95, 65535, 131071, ..., . k must occur by 2^k-1. - Robert G. Wilson v.
Record values: 1, 3, 7, 15, 23, 47, 95, 175, 191, 351, 703, 1375, 1407, 2751, 5503, 10943, 11007, 21887, 22015, 43775, 87423, 87551, 174847, 175103, 349695, 699135, 699391, 1398271, 1398783, 2796543, 2797567, 5592575, 5593087, 11185151, 11186175, ..., . - Robert G. Wilson v.
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LINKS
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Index entries for sequences related to binary expansion of n
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FORMULA
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a(n) = A007318(A000120(n),A069010(n)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2008
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MAPLE
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A000120 := proc(n) local i ; add(i, i=convert(n, base, 2)) ; end: A069010 := proc(n) local b, c, i ; if n = 0 then RETURN(0) ; fi ; b := convert(n, base, 2) ; c := 0 ; if nops(b) > 1 then for i from 1 to nops(b) do if op(i, b) <> op(i-1, b) then c := c+1 ; fi ; od: fi ; op(1, b)+floor(c/2) ; end: A136277 := proc(n) binomial(A000120(n), A069010(n)) ; end: seq(A136277(n), n=0..120) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2008
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MATHEMATICA
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f[n_] := Block[{id = IntegerDigits[n, 2]}, Binomial[ Count[id, 1], Floor[(Length@ Split@ id + 1)/2]]]; Array[f, 100] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A107345.
Sequence in context: A089309 A126387 A038374 this_sequence A133233 A116361 A106796
Adjacent sequences: A136274 A136275 A136276 this_sequence A136278 A136279 A136280
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KEYWORD
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nonn,easy
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AUTHOR
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Neven Juric (neven.juric(AT)apis-it.hr), Apr 01 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Robert G. Wilson v, (rgwv@rgwv.com), Apr 01 2008
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