Triihuktaal

Det ${\displaystyle n}$-st triihuktaal as det sum auer a taalen faan 1 bit ${\displaystyle n}$.

${\displaystyle {\begin{aligned}\Delta _{1}&=1&=&\ 1\\\Delta _{2}&=1+2&=&\ 3\\\Delta _{3}&=1+2+3&=&\ 6\\\Delta _{4}&=1+2+3+4&=&\ 10\\&\qquad \vdots &\end{aligned}}}$

Dü könst det sum uk bereegne mä Gauß sin sumenreegel:

${\displaystyle \Delta _{n}={\frac {n\cdot (n+1)}{2}}}$

10 + 15 = 25

(1) Tau efterfulgin triihuktaalen san en kwadroottaal

Üüb det bil rochts könst dü sä, hü tau efterfulgin triihuktaalen leewen tu en kwadroot tuupsaat wurd kön.

Bispal: ${\displaystyle \Delta _{4}=10}$ an ${\displaystyle \Delta _{5}=15}$ san tuup det kwadroottaal 25.

Bereegnang:

${\displaystyle {\begin{aligned}\Delta _{n-1}+\Delta _{n}&={\frac {n(n-1)}{2}}+{\frac {(n+1)n}{2}}\\&=n^{2}\end{aligned}}}$