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

Author

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

Keywords

• nonn
• easy

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

Crossrefs

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

Programs

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 *)

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

Extensions

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