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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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

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

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

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

Sequence in context: A072577 A231182 A231181 * A057520 A060423 A037951

Adjacent sequences:  A259772 A259773 A259774 * A259776 A259777 A259778

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Jul 05 2015

STATUS

approved

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Last modified August 24 22:39 EDT 2019. Contains 326314 sequences. (Running on oeis4.)