A101473 Boustrophedon transform of the Jacobsthal numbers.

0, 1, 3, 9, 31, 111, 453, 2059, 10571, 60651, 386253, 2704659, 20661411, 170990691, 1523975053, 14552848059, 148234015051, 1604267622731, 18383552327853, 222363321668259, 2831217743661491, 37850593064646771, 530121590756400653

Offset

0,3

Comments

Binomial transform of A101474.

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) = (A000752(n) - A062162(n))/3.

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

Prog

(Python)
from itertools import accumulate, islice
def A101473_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
A101473_list = list(islice(A101473_gen(), 30)) # Chai Wah Wu, Jun 11 2022

Crossrefs

Cf. A000752, A001045, A062162, A101474.

Sequence in context: A049174 A209335 A049159 * A056334 A063032 A056335

Adjacent sequences: A101470 A101471 A101472 * A101474 A101475 A101476

Keyword

easy,nonn

Author

Paul Barry, Jan 21 2005

Status

approved