A259914 Staircase path through the array P(n,k) of the k-th partial sums of cubes (A000578).

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

Author

Luciano Ancora, Jul 08 2015

Keywords

• nonn
• easy

Comments

The term "stepped path" in the name field is the same used in A001405 and A259775.

Examples

			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
		

Crossrefs

Cf. A000537, A024166, A101094, A101097, A101102, A254469.

Programs

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}]

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