A136277 From the binary representation of n: binomial(number of ones, number of blocks of contiguous ones).

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

Offset

0,4

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Formula

a(n) = A007318(A000120(n),A069010(n)). - R. J. Mathar, Apr 01 2008

a(n) = A181591(A005940(1+n)). - Antti Karttunen, May 29 2017

Maple

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, Apr 01 2008

Mathematica

f[n_] := Block[{id = IntegerDigits[n, 2]}, Binomial[ Count[id, 1], Floor[(Length@ Split@ id + 1)/2]]]; Array[f, 100] (* Robert G. Wilson v *)

Crossrefs

Cf. A000120, A007318, A069010, A107345, A181591, A278222.

Sequence in context: A325757 A161161 A350357 * A133233 A174430 A116361

Adjacent sequences: A136274 A136275 A136276 * A136278 A136279 A136280

Keyword

nonn,easy

Author

Neven Juric (neven.juric(AT)apis-it.hr), Apr 01 2008

Extensions

More terms from R. J. Mathar and Robert G. Wilson v, Apr 01 2008

Status

approved