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%I #17 Jul 16 2015 06:28:40
%S 1,5,6,20,27,77,112,294,450,1122,1782,4290,7007,16445,27456,63206,
%T 107406,243542,419900,940576,1641486,3640210,6418656,14115100,
%U 25110020,54826020,98285670,213286590,384942375
%N Stepped path in P(k,n) array of k-th partial sums of squares (A000290).
%C The term "stepped path" in the name field is the same used in A001405.
%C Interleaving of terms of the sequences A220101 and A129869. - _Michel Marcus_, Jul 05 2015
%F 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
%e The array of k-th partial sums of squares begins:
%e [1], [5], 14, 30, 55, 91, ... A000330
%e 1, [6], [20], 50, 105, 196, ... A002415
%e 1, 7, [27], [77], 182, 378, ... A005585
%e 1, 8, 35, [112], [294], 672, ... A040977
%e 1, 9, 44, 156, [450], [1122], ... A050486
%e 1, 10, 54, 210, 660, [1782], ... A053347
%e This is essentially A110813 without its first two columns.
%t 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}]
%Y Cf. A000330, A002415, A005585, A040977, A050486, A053347.
%K nonn,easy
%O 1,2
%A _Luciano Ancora_, Jul 05 2015
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