A334012
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.
Original entry on oeis.org
From _Seiichi Manyama_, May 16 2021: (Start)
Let S(k, m) denote the sum of m octagonal numbers starting from k*(3*k-2). We have
a(1) = S(1, 1);
a(2) = S(19, 1) = S(1, 10);
a(3) = S(45, 1) = S(11, 9) = S(1, 18). (End)
Cf.
A000567,
A054859,
A068314,
A186337,
A298467,
A322637,
A334007,
A334008,
A334010,
A334011,
A344376.
A334008
a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero pentagonal numbers in exactly n ways.
Original entry on oeis.org
1, 287, 472320, 89051435880
Offset: 1
Let S(k, m) denote the sum of m pentagonal numbers starting from the k-th. We have
a(1) = S(1, 1);
a(2) = S(14, 1) = S(2, 7);
a(3) = S(103, 24) = S(19, 80) = S(67, 41);
a(4) = S(10833, 484) = S(4542, 1936) = S(9153, 660) = S(2817, 3036);
A334010
a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero hexagonal numbers in exactly n ways.
Original entry on oeis.org
1, 703, 274550, 11132303325
Offset: 1
Let S(k, m) denote the sum of m hexagonal numbers starting from the k-th. We have
a(1) = S(1, 1);
a(2) = S(19, 1) = S(13, 2);
a(3) = S(62, 25) = S(184, 4) = S(25, 51);
a(4) = S(3065, 505) = S(22490, 11) = S(1215, 1430) = S(1938, 946).
A334011
a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero heptagonal numbers in exactly n ways.
Original entry on oeis.org
1, 872, 8240232, 263346158075
Offset: 1
Let S(k, m) denote the sum of m heptagonal numbers starting from the k-th. We have
a(1) = S(1, 1);
a(2) = S(13, 2) = S(3, 8);
a(3) = S(133, 98) = S(479, 14) = S(168, 77);
a(4) = S(6773, 1785) = S(810, 6006) = S(7467, 1547) = S(38758, 70).
A343777
a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero n-gonal numbers in exactly n ways.
Original entry on oeis.org
2180, 554503705
Offset: 3
A368076
a(n) is the least integer that can be expressed as the difference of two positive tetrahedral numbers in exactly n ways.
Original entry on oeis.org
3, 36, 2180, 10053736
Offset: 1
a(2) = 36: 36 = 56 - 20 = 120 - 84.
A329236
a(n) is the least integer that can be expressed as the sum of one or more consecutive centered triangular numbers in exactly n ways.
Original entry on oeis.org
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