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

1,2

Links

Table of n, a(n) for n=1..16.

Example

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

Prog

(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

Crossrefs

Cf. A181132, A000788.

Sequence in context: A270497 A025958 A199674 * A022741 A225966 A057614

Adjacent sequences: A369329 A369330 A369331 * A369333 A369334 A369335

Keyword

nonn,base

Author

Tamas Sandor Nagy, Jan 20 2024

Extensions

More terms from Andrew Howroyd, Jan 20 2024

Status

approved