A281228 Expansion of (Sum_{k>=0} x^(3^k))^2 [even terms only].

0, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,3

Comments

Number of ways to write 2n as an ordered sum of two powers of 3.

First bisection of self-convolution of characteristic function of powers of 3.

Links

Table of n, a(n) for n=0..105.

Index entries for sequences related to compositions

Formula

G.f.: (Sum_{k>=0} x^(3^k))^2 [even terms only].

Example

G.f. = x^2 + 2*x^4 + x^6 + 2*x^10 + 2*x^12 + x^18 + 2*x^28 + 2*x^30 + 2*x^36 + ...
a(2) = 2 because we have [3, 1] and [1, 3].

Mathematica

Take[CoefficientList[Series[Sum[x^3^k, {k, 0, 15}]^2, {x, 0, 260}], x], {1, -1, 2}]

Crossrefs

Cf. A000244, A055235, A073267, A078932.

Sequence in context: A025253 A356261 A356262 * A284575 A112178 A134663

Adjacent sequences: A281225 A281226 A281227 * A281229 A281230 A281231

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 18 2017

Status

approved