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%I #24 Sep 08 2022 08:46:12
%S 1,17,99,373,1115,2901,6907,15509,33483,70405,145451,296997,601819,
%T 1213493,2439195,4893301,9804587,19630629,39286603,78602885,157240251,
%U 314520277,629086139,1258224213,2516507275,5033080901,10066236267,20132555749,40265204123
%N a(n) = 75*(2^n - 1) - 4*n^3 - 18*n^2 - 52*n.
%C See the first comment of A257448.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).
%F G.f.: -x*(1 + x)*(1 + 10*x + x^2)/((-1 + x)^4*(-1 + 2*x)).
%F a(n) = 6*a(n-1) -14*a(n-2) +16*a(n-3) -9*a(n-4) +2*a(n-5) for n>5.
%e This sequence provides the antidiagonal sums of the array:
%e 1, 16, 81, 256, 625, 1296, ... A000583
%e 1, 17, 98, 354, 979, 2275, ... A000538
%e 1, 18, 116, 470, 1449, 3724, ... A101089
%e 1, 19, 135, 605, 2054, 5778, ... A101090
%e 1, 20, 155, 760, 2814, 8592, ... A101091
%e 1, 21, 176, 936, 3750, 12342, ... A254681
%e ...
%e See also A254681 (Example field).
%t Table[75 (2^n - 1) - 4 n^3 - 18 n^2 - 52 n, {n, 30}]
%o (Magma) [75*(2^n-1)-4*n^3-18*n^2-52*n: n in [1..30]]; // _Vincenzo Librandi_, Apr 24 2015
%Y Cf. A000225, A000670, A050488, A208744, A257448, A257450.
%K nonn,easy
%O 1,2
%A _Luciano Ancora_, Apr 23 2015
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