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

0,4

Comments

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

Links

Table of n, a(n) for n=0..24.

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

Prog

(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

Crossrefs

Cf. A001045.

Sequence in context: A146248 A074000 A067645 * A298836 A252284 A259367

Adjacent sequences: A101471 A101472 A101473 * A101475 A101476 A101477

Keyword

easy,nonn

Author

Paul Barry, Jan 21 2005

Status

approved