A285103 Number of odd terms on row n of A053632: a(n) = A000120(A068052(n)).

1, 2, 4, 6, 6, 12, 12, 16, 22, 28, 32, 30, 36, 52, 48, 62, 62, 68, 88, 104, 116, 108, 128, 128, 132, 168, 160, 168, 200, 204, 240, 232, 242, 284, 300, 324, 332, 348, 352, 352, 412, 440, 400, 466, 460, 516, 496, 566, 582, 580, 608, 646, 676, 736, 716, 782, 728, 816, 832, 856, 916, 924, 948, 1034, 1008, 1044, 1096, 1154, 1112, 1212, 1204, 1188

Offset: 0

Author

Antti Karttunen, Apr 15 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000 (first 257 terms from Antti Karttunen)

Crossrefs

Number of odd term on row n of A053632.

Cf. A000120, A000124, A001221, A001222, A068052, A285102, A285104, A285105.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1,
      (t-> Bits[Xor](2^n*t, t))(b(n-1)))
    end:
a:= n-> convert(Bits[Split](b(n)), `+`):
seq(a(n), n=0..71);  # Alois P. Heinz, Mar 07 2024

Mathematica

b[n_] := b[n] = If[n == 0, 1, With[{t = b[n-1]}, BitXor[2^n*t, t]]];
a[n_] := DigitCount[b[n], 2, 1];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 17 2024, after Alois P. Heinz *)

Python

# uses [A000120]
l=[1]
for n in range(1, 101):
    x = l[n - 1]
    l.append(x^(2**n*x))
print([A000120(k) for k in l]) # Indranil Ghosh, Jun 28 2017

Scheme

(define (A285103 n) (A000120 (A068052 n)))

Formula

a(n) = A000120(A068052(n)).

a(n) = A001221(A285102(n)) = A001222(A285102(n)).

A285104(n) = 2^n - a(n).

A000124(n) = a(n) + A285105(n).