The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #14 Jul 16 2015 08:39:32
%S 1,9,10,46,57,203,272,846,1200,3432,5082,13728,21021,54483,85696,
%T 215254,346086,848198,1388900,3337236,5549786,13119614,22108704,
%U 51557260,87885070,202588830,348817770,796117860,1382941125,3129153795
%N Staircase path through the array P(n,k) of the k-th partial sums of cubes (A000578).
%C The term "stepped path" in the name field is the same used in A001405 and A259775.
%F 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 The array begins:
%e [1], [9], 36, 100, 225, 441, ... A000537
%e 1, [10], [46], 146, 371, 812, ... A024166
%e 1, 11, [57], [203], 574, 1386, ... A101094
%e 1, 12, 69, [272], [846], 2232, ... A101097
%e 1, 13, 82, 354, [1200], [3432], ... A101102
%e 1, 14, 96, 450, 1650, [5082], ... A254469
%t Table[DifferenceRoot[Function[{a, n},
%t {(-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 Cf. A000537, A024166, A101094, A101097, A101102, A254469.
%K nonn,easy
%O 1,2
%A _Luciano Ancora_, Jul 08 2015