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
Programs
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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}] -
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
Extensions
a(29)-a(37) from Chai Wah Wu, Feb 05 2024