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A308985
Expansion of Product_{k>=0} (1 + 2*x^(2^k))^2.
1
1, 4, 8, 16, 24, 32, 48, 64, 88, 96, 128, 128, 176, 192, 256, 256, 344, 352, 448, 384, 512, 512, 640, 512, 688, 704, 896, 768, 1024, 1024, 1280, 1024, 1368, 1376, 1728, 1408, 1856, 1792, 2176, 1536, 2048, 2048, 2560, 2048, 2688, 2560, 3072, 2048, 2736, 2752, 3456
OFFSET
0,2
COMMENTS
Self-convolution of A001316.
FORMULA
a(n) = Sum_{k=0..n} 2^(A000120(k)+A000120(n-k)).
a(n) = A001316(n) * Sum_{k=0..n} 2^(A007814(binomial(n,k))).
G.f. A(x) satisfies: A(x) = (1 + 2*x)^2 * A(x^2). - Ilya Gutkovskiy, Jul 09 2019
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 + 2 x^(2^k))^2, {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
a[n_] := a[n] = Sum[2^(DigitCount[k, 2, 1] + DigitCount[n - k, 2, 1]), {k, 0, n}]; Table[a[n], {n, 0, 50}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 04 2019
STATUS
approved