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binomial_coefficient_over_the_complex_numbers [2016/05/12 19:00] nikolaj |
binomial_coefficient_over_the_complex_numbers [2016/05/12 19:21] nikolaj |
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| From this it's also clear that ${n\choose{k}}$ is a sum of 1's, i.e. an integer. | From this it's also clear that ${n\choose{k}}$ is a sum of 1's, i.e. an integer. | ||
| + | |||
| + | <code> | ||
| + | (* Random generalization of linear such recursive schemes *) | ||
| + | |||
| + | F[m_, 0] = a; | ||
| + | F[0, m_] = b; | ||
| + | F[m_, m_] = c; | ||
| + | |||
| + | F[n_, k_] := A*F[n, k - 1] + B*F[n - 1, k] + C*F[n - 1, k - 1] | ||
| + | |||
| + | Table[{n, k, F[n, k]}, {n, 0, 4}, {k, 0, 4}] // TableForm | ||
| + | </code> | ||
| === Reference === | === Reference === | ||
