A334035 a(n) is the least integer that can be expressed as the difference of two hexagonal numbers in exactly n ways.

1, 45, 225, 585, 2415, 4725, 9945, 10395, 31185, 28665, 45045, 58905, 143325, 257985, 135135, 225225, 329175, 487305, 405405, 831285, 1091475, 675675, 1396395, 1576575, 2927925, 3132675, 2436525, 2027025, 2567565, 2297295, 6235515, 5360355, 4729725, 3828825, 10503675

Offset: 1

Author

Ilya Gutkovskiy, Apr 12 2020

Keywords

• nonn

Comments

The least integer that can be expressed as the sum of one or more consecutive numbers congruent to 1 mod 4 in exactly n ways.

Index of first occurrence of n in A333816.

Links

• Eric Weisstein's World of Mathematics, Hexagonal Number
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A000384, A016813, A038547, A068314, A333816, A334010, A334034, A334036, A334037.

Programs

Mathematica

nmax = 10000; A333816 = Rest[CoefficientList[Series[Sum[x^(k*(2*k - 1))/(1 - x^(4*k)), {k, 1, 1 + Sqrt[nmax/2]}], {x, 0, nmax}], x]]; Flatten[Table[FirstPosition[A333816, k], {k, 1, Max[A333816]}]] (* Vaclav Kotesovec, Apr 19 2020 *)

Extensions

More terms from Jinyuan Wang, Apr 13 2020