cp's OEIS Frontend

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

%I A136277 #14 May 29 2017 06:17:23
%S A136277 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,
%T A136277 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,
%U A136277 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
%N A136277 From the binary representation of n: binomial(number of ones, number of blocks of contiguous ones).
%C A136277 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_
%C A136277 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_
%H A136277 Antti Karttunen, <a href="/A136277/b136277.txt">Table of n, a(n) for n = 0..8192</a>
%H A136277 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A136277 a(n) = A007318(A000120(n),A069010(n)). - _R. J. Mathar_, Apr 01 2008
%F A136277 a(n) = A181591(A005940(1+n)). - _Antti Karttunen_, May 29 2017
%p A136277 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
%t A136277 f[n_] := Block[{id = IntegerDigits[n, 2]}, Binomial[ Count[id, 1], Floor[(Length@ Split@ id + 1)/2]]]; Array[f, 100] (* _Robert G. Wilson v_ *)
%Y A136277 Cf. A000120, A007318, A069010, A107345, A181591, A278222.
%K A136277 nonn,easy
%O A136277 0,4
%A A136277 Neven Juric (neven.juric(AT)apis-it.hr), Apr 01 2008
%E A136277 More terms from _R. J. Mathar_ and _Robert G. Wilson v_, Apr 01 2008