Predstavimo nov razred totalno pozitivnih Toeplitzevih matrik, sestavljenih iz nedavno vpeljanih hiperfibonaccijevih števil ▫$r$▫-te generacije. Pokažemo, da so vsa zaporedja ▫$F_n^{(r)}$▫ ...hiperfibonaccijevih števil ▫$r$▫-te generacije log-konkavna za ▫$r \ge 1$▫ in dovolj velike ▫$n$▫.
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