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<p>Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:</p><p><div style="display: inline-grid; text-align: center; grid-template-columns: repeat(3, minmax(117px, 12%)); grid-template-rows: auto;"><div>Triangle</div><div>T<sub>n</sub>=<var>n</var>(<var>n</var>+1)/2</div><div>1, 3, 6, 10, 15, ...</div></div></p>
<p><div style="display: inline-grid; text-align: center; grid-template-columns: repeat(3, minmax(117px, 12%)); grid-template-rows: auto;"><div>Pentagonal</div><div>P<sub>n</sub>=<var>n</var>(3<var>n</var>−1)/2</div><div>1, 5, 12, 22, 35, ...</div></div></p>
<p><div style="display: inline-grid; text-align: center; grid-template-columns: repeat(3, minmax(117px, 12%)); grid-template-rows: auto;"><div>Hexagonal</div><div>H<sub>n</sub>=<var>n</var>(2<var>n</var>−1)</div><div>1, 6, 15, 28, 45, ...</div></div></p>
<p>It can be verified that T<sub>285</sub> = P<sub>165</sub> = H<sub>143</sub> = 40755.</p>
<p>Find the next triangle number that is also pentagonal and hexagonal.</p></section>

Problem 45: Triangular, pentagonal, and hexagonal