A101625 A bisection of the Stern-Jacobsthal numbers.

0, 1, 1, 5, 1, 21, 17, 69, 1, 277, 273, 1349, 257, 5141, 4113, 16453, 1, 65813, 65809, 329029, 65793, 1381397, 1118225, 4538437, 65537, 18088213, 17826065, 88081733, 16777473, 335549461, 268439569, 1073758277, 1, 4295033109, 4295033105

Offset: 0

Author

Paul Barry, Dec 10 2004

Keywords

• easy
• nonn

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002450.

Programs

Python

prpr = 0
prev = 1
for i in range(99):
    current = (prev)^(prpr*4)
    print(prpr, end=',')
    prpr = prev
    prev = current
# Alex Ratushnyak, May 06 2012

Formula

a(n) = Sum_{k=0..n} (binomial(2n-k, k-1) mod 2)2^(k-1);

a(n) = A101624(2n+1).

a(0)=0, a(1)=1, a(n) = a(n-1) XOR (a(n-2)*4), where XOR is the bitwise exclusive-OR operator. - Alex Ratushnyak, May 06 2012

a(n+1) = Sum_{k=0..n} A106344(n,k)*4^(n-k). - Philippe Deléham, May 27 2012