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A259914
Staircase path through the array P(n,k) of the k-th partial sums of cubes (A000578).
0
1, 9, 10, 46, 57, 203, 272, 846, 1200, 3432, 5082, 13728, 21021, 54483, 85696, 215254, 346086, 848198, 1388900, 3337236, 5549786, 13119614, 22108704, 51557260, 87885070, 202588830, 348817770, 796117860, 1382941125, 3129153795
OFFSET
1,2
COMMENTS
The term "stepped path" in the name field is the same used in A001405 and A259775.
FORMULA
Conjecture: 2*(n+7)*(145672*n^2-236343*n+123525)*a(n) +(-78613*n^3-794662*n^2+327391*n+20220)*a(n-1) +2*(-582688*n^3-1889455*n^2-2148719*n-832650)*a(n-2) +4*(n-1)*(78613*n^2+133361*n+64050)*a(n-3) = 0. - R. J. Mathar, Jul 16 2015
EXAMPLE
The array begins:
[1], [9], 36, 100, 225, 441, ... A000537
1, [10], [46], 146, 371, 812, ... A024166
1, 11, [57], [203], 574, 1386, ... A101094
1, 12, 69, [272], [846], 2232, ... A101097
1, 13, 82, 354, [1200], [3432], ... A101102
1, 14, 96, 450, 1650, [5082], ... A254469
MATHEMATICA
Table[DifferenceRoot[Function[{a, n},
{(-650880 - 1496112*n - 1426512*n^2 - 722164*n^3 - 204716*n^4 - 30812*n^5 - 1924*n^6)*a[n] + (-56736 - 140412*n - 132006*n^2 - 58114*n^3 - 12090*n^4 - 962*n^5)*a[1 + n] + (78624 + 229884*n + 273800*n^2 + 167579*n^3 + 54567*n^4 + 8665*n^5 + 481*n^6)*a[2 + n] == 0, a[1] == 1, a[2] == 9}]][n], {n, 30}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jul 08 2015
STATUS
approved