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Nanostructured silicon carbide (SiC) materials are expected to have bright prospect in application as high-performance electrode materials with excellent charge–discharge cycling stability. However, the exploration of SiC-based micro-supercapacitors (MSCs) still remains a grand challenge seriously hampered by low areal capacities and complicated multistep production process. Herein, we report that rationally designed SiC/C nanocomposite with hierarchical porous structure and improved electrical conductivity has been realized by a facile and rapid carbothermic reduction using silica sol and sucrose as silicon and carbon source. The amorphous carbon between SiC nanoparticles (NPs) contributes to enlarged surface areas and excellent conductivity, not only ensuring intimate contact between the electrolyte and the electrode but also providing an effective ion highway for electrolyte ions. As a result, MSCs based on SiC/C nanocomposite (Si/C mass ratio of 1:1.5) demonstrate an optimal specific areal capacitance of 11.8 mF cm−2 at 2 mV s−1, outstanding flexibility (104.5% retention of initial capacitance at 180° bending), and superior integration. Most notably, the capacitance remains at 97.3% of the initial value after 50000 charging/discharging cycles, superior to that of most advanced SiC-based MSCs ever reported. This work demonstrates an effective design for hierarchical porous SiC/C nanocomposite for energy storage, which gives significant inspirations on the exploration of high-performance SiC-based MSCs.

In “Proofs That Really Count” A. T. Benjamin and J. J. Quinn provided several identities involving Fibonacci numbers and left some unproven ones. They posed questions to find the combinatorial proofs of these identities. Among these identities, the following one caught our attention because of concerning parity: ∑ k = 0 n ( − 1 ) k f k = 1 + ( − 1 ) n f n − 1 . . Krzykowski found that the coverings in an area with dimension 2 × n can be enumerated by Fibonacci numbers. In this paper, we give an involution throughout the interpretation of Fibonacci numbers given by Krzywkowski to explain the above identity and answer the question provided by Benjamin and Quinn.