A259775 Stepped path in P(k,n) array of k-th partial sums of squares (A000290).

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

Author

Luciano Ancora, Jul 05 2015

Keywords

• nonn
• easy

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

Examples

			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.
		

Crossrefs

Cf. A000330, A002415, A005585, A040977, A050486, A053347.

Programs

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}]

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