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
Programs
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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
Formula
E.g.f.: (sec(x) + tan(x))*(exp(2*x) - exp(-x))/3.
a(n) ~ n! * 2^(n+2) * (exp(Pi) - exp(-Pi/2)) / (3 * Pi^(n+1)). - Vaclav Kotesovec, Jun 12 2015
Comments