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.

1, 17, 186, 12234, 605714, 30143621, 865062888, 374978871766, 92420578210888, 22764626902276757, 4227156427366610576, 1076625258046594762034, 196829039855755478065982, 34737980525681450161565604, 3519580168264415862502129296, 8186117385516870986118141242073

Offset: 1

Author

Tamas Sandor Nagy, Jan 20 2024

Keywords

• nonn
• base

Examples

			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:
       1     1
      10     2
      11     3
     101     5
     110     6
     111     7
    1011    11
    1101    13
    1110    14
    1111    15
   10111    23
   11011    27
   11101    29
   11110    30
           ---
   Total:  186
		

Crossrefs

Cf. A181132, A000788.

Programs

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

Extensions

More terms from Andrew Howroyd, Jan 20 2024