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A259775
Stepped path in P(k,n) array of k-th partial sums of squares (A000290).
1
1, 5, 6, 20, 27, 77, 112, 294, 450, 1122, 1782, 4290, 7007, 16445, 27456, 63206, 107406, 243542, 419900, 940576, 1641486, 3640210, 6418656, 14115100, 25110020, 54826020, 98285670, 213286590, 384942375
OFFSET
1,2
COMMENTS
The term "stepped path" in the name field is the same used in A001405.
Interleaving of terms of the sequences A220101 and A129869. - Michel Marcus, Jul 05 2015
FORMULA
Conjecture: -(n+5)*(13*n-11)*a(n) +(8*n^2+39*n-35)*a(n-1) +2*(26*n^2+48*n+25)*a(n-2) -4*(8*n+5)*(n-1)*a(n-3)=0. - R. J. Mathar, Jul 16 2015
EXAMPLE
The array of k-th partial sums of squares begins:
[1], [5], 14, 30, 55, 91, ... A000330
1, [6], [20], 50, 105, 196, ... A002415
1, 7, [27], [77], 182, 378, ... A005585
1, 8, 35, [112], [294], 672, ... A040977
1, 9, 44, 156, [450], [1122], ... A050486
1, 10, 54, 210, 660, [1782], ... A053347
This is essentially A110813 without its first two columns.
MATHEMATICA
Table[DifferenceRoot[Function[{a, n}, {(-9168 - 14432*n - 8412*n^2 - 2152*n^3 - 204*n^4)*a[n] +(-1332 - 1902*n - 792*n^2 - 102*n^3)*a[1 + n] + (2100 + 3884*n + 2493*n^2 + 640*n^3 + 51*n^4)*a[2 + n] == 0, a[1] == 1 , a[2] == 5}]][n], {n, 29}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jul 05 2015
STATUS
approved