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

1,2

Comments

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

Links

Table of n, a(n) for n=1..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

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

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

Sequence in context: A041172 A248353 A156857 * A368047 A037954 A271062

Adjacent sequences: A259911 A259912 A259913 * A259915 A259916 A259917

Keyword

nonn,easy

Author

Luciano Ancora, Jul 08 2015

Status

approved