The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A334035 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A334035

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

#9 by Vaclav Kotesovec at Sun Apr 19 08:09:50 EDT 2020

STATUS

editing

approved

#8 by Vaclav Kotesovec at Sun Apr 19 08:09:38 EDT 2020

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 *)

STATUS

approved

editing

#7 by Susanna Cuyler at Mon Apr 13 08:02:07 EDT 2020

STATUS

proposed

approved

#6 by Jinyuan Wang at Mon Apr 13 01:43:30 EDT 2020

STATUS

editing

proposed

#5 by Jinyuan Wang at Mon Apr 13 01:43:24 EDT 2020

DATA

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

KEYWORD

nonn,more,changed

EXTENSIONS

More terms from Jinyuan Wang, Apr 13 2020

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Sun Apr 12 23:42:15 EDT 2020

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Sun Apr 12 23:25:03 EDT 2020

CROSSREFS

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

#2 by Ilya Gutkovskiy at Sun Apr 12 23:12:23 EDT 2020

NAME

allocated for Ilya Gutkovskiya(n) is the least integer that can be expressed as the difference of two hexagonal numbers in exactly n ways.

DATA

1, 45, 225, 585, 2415, 4725, 9945, 10395, 31185, 28665, 45045, 58905, 143325, 257985, 135135, 225225, 329175

OFFSET

1,2

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, <a href="http://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>

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

CROSSREFS

Cf. A000384, A016813, A038547, A068314, A333816, A334010.

KEYWORD

allocated

nonn,more

AUTHOR

Ilya Gutkovskiy, Apr 12 2020

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sun Apr 12 23:12:23 EDT 2020

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved