A101474 Boustrophedon transform of the signed Jacobsthal numbers.

0, 1, 1, 3, 9, 21, 111, 393, 2309, 12321, 81071, 560033, 4301109, 35526921, 316858231, 3025055673, 30815437909, 333492212321, 3821573586591, 46224758487313, 588552491006709, 7868364598774521, 110201454736846151, 1613597716238974953, 24653957361927031509

Offset: 0

Author

Paul Barry, Jan 21 2005

Keywords

• easy
• nonn

Comments

Boustrophedon transform of (-1)^n*A001045(n). Binomial transform is A101473.

Crossrefs

Cf. A001045.

Programs

Python

from itertools import accumulate, islice
def A101474_gen(): # generator of terms
    blist, a, b = tuple(), 0, -1
    while True:
        yield (blist := tuple(accumulate(reversed(blist),initial=a)))[-1]
        a, b = -b, -2*a-b
A101474_list = list(islice(A101474_gen(),30)) # Chai Wah Wu, Jun 11 2022

Formula

E.g.f.: (sec(x)+tan(x))*(exp(x)-exp(-2*x))/3.

a(n) ~ n! * (exp(3*Pi/2)-1) * 2^(n+2) / (3 * exp(Pi) * Pi^(n+1)). - Vaclav Kotesovec, Jun 12 2015