A367736 a(0) = 1; for n > 0, a(n) is the coefficient of x^a(n-1) in the expansion of Product_{k=0..n-1} (x^a(k) + 1 + 1/x^a(k)).

1, 1, 2, 4, 6, 11, 19, 32, 58, 97, 163, 290, 501, 856, 1483, 2561, 4424, 7652, 13273, 23024, 39784, 69001, 119614, 207042, 358746, 621117, 1075865, 1864050, 3227724, 5590548, 9682402, 16770033, 29049713, 50310453, 87142439, 150939346, 261424583, 452810957

Offset

0,3

Links

Table of n, a(n) for n=0..37.

Mathematica

a[0] = 1; a[n_] := a[n] = Coefficient[Product[x^a[k] + 1 + 1/x^a[k], {k, 0, n - 1}], x, a[n - 1]]; Table[a[n], {n, 0, 28}]

Prog

(Python)
from itertools import islice
from collections import Counter
def A367736_gen(): # generator of terms
    c, b = {0:1}, 1
    while True:
        yield b
        d = Counter(c)
        for k in c:
            e = c[k]
            d[k+b] += e
            d[k-b] += e
        c = d
        b = c[b]
A367736_list = list(islice(A367736_gen(), 20)) # Chai Wah Wu, Feb 05 2024

Crossrefs

Cf. A063890, A265853, A316706.

Sequence in context: A115993 A136424 A116732 * A048239 A000786 A289080

Adjacent sequences: A367733 A367734 A367735 * A367737 A367738 A367739

Keyword

nonn,more

Author

Ilya Gutkovskiy, Jan 24 2024

Extensions

a(29)-a(37) from Chai Wah Wu, Feb 05 2024

Status

approved