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

%I A259914 #14 Jul 16 2015 08:39:32
%S A259914 1,9,10,46,57,203,272,846,1200,3432,5082,13728,21021,54483,85696,
%T A259914 215254,346086,848198,1388900,3337236,5549786,13119614,22108704,
%U A259914 51557260,87885070,202588830,348817770,796117860,1382941125,3129153795
%N A259914 Staircase path through the array P(n,k) of the k-th partial sums of cubes (A000578).
%C A259914 The term "stepped path" in the name field is the same used in A001405 and A259775.
%F A259914 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
%e A259914 The array begins:
%e A259914 [1], [9],  36,   100,   225,    441,  ...  A000537
%e A259914 1,  [10], [46],  146,   371,    812,  ...  A024166
%e A259914 1,   11,  [57], [203],  574,   1386,  ...  A101094
%e A259914 1,   12,   69,  [272], [846],  2232,  ...  A101097
%e A259914 1,   13,   82,   354, [1200], [3432], ...  A101102
%e A259914 1,   14,   96,   450,  1650,  [5082], ...  A254469
%t A259914 Table[DifferenceRoot[Function[{a, n},
%t A259914          {(-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}]
%Y A259914 Cf. A000537, A024166, A101094, A101097, A101102, A254469.
%K A259914 nonn,easy
%O A259914 1,2
%A A259914 _Luciano Ancora_, Jul 08 2015