A308985 Expansion of Product_{k>=0} (1 + 2*x^(2^k))^2.

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.

Links

Table of n, a(n) for n=0..50.

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

Cf. A000120, A001316, A006046, A007814, A308986.

Sequence in context: A270345 A335668 A181823 * A046059 A355392 A290498

Adjacent sequences: A308982 A308983 A308984 * A308986 A308987 A308988

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 04 2019

Status

approved