A038192 Bisection of A001317.

3, 15, 51, 255, 771, 3855, 13107, 65535, 196611, 983055, 3342387, 16711935, 50529027, 252645135, 858993459, 4294967295, 12884901891, 64424509455, 219043332147, 1095216660735, 3311419785987, 16557098929935, 56294136361779

Offset

0,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..1000

Formula

a(n) = 12*A089893(n) + 3.

a(n+1) = (2 * a(n)) XOR (3 * a(n)), where XOR is the bitwise exclusive or operator. - Federico Provvedi, Sep 14 2023

Mathematica

NestList[BitXor[2#, 3#]&, 3, 30] (* Federico Provvedi, Sep 14 2023 *)

Prog

(PARI) a(n)=sum(k=0, 2*n+1, (binomial(2*n+1, k)%2)<<k) \\ Charles R Greathouse IV, Aug 08 2013
(PARI) A011371(n)=my(s); while(n>>=1, s+=n); s
A047999(n, k)=A011371(n)==A011371(k)+A011371(n-k)
a(n)=n+=n+1; sum(k=0, n, A047999(n, k)<<k) \\ Charles R Greathouse IV, Aug 09 2013
(Python)
def A038192(n): return sum((bool(~(m:=(n<<1)+1)&m-k)^1)<<k for k in range((n+1)<<1)) # Chai Wah Wu, May 02 2023

Crossrefs

Cf. A001317, A089893.

Sequence in context: A231747 A192742 A166035 * A212869 A371481 A332375

Adjacent sequences: A038189 A038190 A038191 * A038193 A038194 A038195

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved