Square Triangular Number - Numerical Data

Numerical Data

As k becomes larger, the ratio tk / sk approaches and the ratio of successive square triangular numbers approaches .

 \begin{array}{rrrrll}
k & N_k & s_k & t_k & t_k/s_k & N_k/N_{k-1} \\
0 & 0 & 0 & 0 & & \\
1 & 1 & 1 & 1 & 1 & \\
2 & 36 & 6 & 8 & 1.33333 & 36\\
3 & 1\,225 & 35 & 49 & 1.4 & 34.02778\\
4 & 41\,616 & 204 & 288 & 1.41176 & 33.97224\\
5 & 1\,413\,721 & 1\,189 & 1\,681 & 1.41379 & 33.97061\\
6 & 48\,024\,900 & 6\,930 & 9\,800 & 1.41414 & 33.97056\\
7 & 1\,631\,432\,881 & 40\,391 & 57\,121 & 1.41420 & 33.97056\\
\end{array}

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