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a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero octagonal numbers in exactly n ways.
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%I #18 Feb 16 2025 08:34:00

%S 1,1045,5985

%N a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero octagonal numbers in exactly n ways.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%e From _Seiichi Manyama_, May 16 2021: (Start)

%e Let S(k, m) denote the sum of m octagonal numbers starting from k*(3*k-2). We have

%e a(1) = S(1, 1);

%e a(2) = S(19, 1) = S(1, 10);

%e a(3) = S(45, 1) = S(11, 9) = S(1, 18). (End)

%Y Cf. A000567, A054859, A068314, A186337, A298467, A322637, A334007, A334008, A334010, A334011, A344376.

%K nonn,hard,more,changed

%O 1,2

%A _Ilya Gutkovskiy_, Apr 12 2020