合成数与卷积斐波那契数
Number of Compositions and Convolved Fibonacci numbers
摘要：
考虑了两类行列式为斐波那契数的上Hessenberg矩阵.计算第一种类型的固定阶的主子式的和使我们得到卷积的斐波那契数。证明了这些数和斐波那契数的一些恒等式。我们还证明了一个自然数与固定个数的1的复合数作为行列式为Fibonacci数的Hessenberg矩阵的特征多项式的系数出现。我们推导出明确的公式，这种组合物的数量，在卷积的斐波那契数。
英文摘要：
We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for Fibonacci numbers are proved. We also show that numbers of compositions of a natural number with fixed number of ones appear as coefficients of characteristic polynomial of a Hessenberg matrix which determinant is a Fibonacci number. We derive the explicit formula for the number of such compositions, in terms of convolutions of Fibonacci numbers.
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