cp's OEIS Frontend

A369332 a(n) is the sum of numbers whose binary forms can be constructed using some or all of the binary digits of 1..n.

%I A369332 #17 Jan 29 2024 19:09:46
%S A369332 1,17,186,12234,605714,30143621,865062888,374978871766,92420578210888,
%T A369332 22764626902276757,4227156427366610576,1076625258046594762034,
%U A369332 196829039855755478065982,34737980525681450161565604,3519580168264415862502129296,8186117385516870986118141242073
%N A369332 a(n) is the sum of numbers whose binary forms can be constructed using some or all of the binary digits of 1..n.
%e A369332 For a(3) = 186, the binary forms of n = 1, 2 and 3 are 1, 10 and 11. These together contain four 1's and one 0. The possible combinations to construct binary numbers of these are below with their equivalent decimal values:
%e A369332        1     1
%e A369332       10     2
%e A369332       11     3
%e A369332      101     5
%e A369332      110     6
%e A369332      111     7
%e A369332     1011    11
%e A369332     1101    13
%e A369332     1110    14
%e A369332     1111    15
%e A369332    10111    23
%e A369332    11011    27
%e A369332    11101    29
%e A369332    11110    30
%e A369332            ---
%e A369332    Total:  186
%o A369332 (PARI) a(n)={my(w=0,b=0); for(i=1, n, w+=hammingweight(i); b+=logint(i,2)+1); sum(j=0, w-1, sum(k=0, b-w, my(t=j+k);if(t, binomial(t,j)*(2^t + j*(2^t-1)/t), 1) ))} \\ _Andrew Howroyd_, Jan 20 2024
%Y A369332 Cf. A181132, A000788.
%K A369332 nonn,base
%O A369332 1,2
%A A369332 _Tamas Sandor Nagy_, Jan 20 2024
%E A369332 More terms from _Andrew Howroyd_, Jan 20 2024