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A257449
a(n) = 75*(2^n - 1) - 4*n^3 - 18*n^2 - 52*n.
2
1, 17, 99, 373, 1115, 2901, 6907, 15509, 33483, 70405, 145451, 296997, 601819, 1213493, 2439195, 4893301, 9804587, 19630629, 39286603, 78602885, 157240251, 314520277, 629086139, 1258224213, 2516507275, 5033080901, 10066236267, 20132555749, 40265204123
OFFSET
1,2
COMMENTS
See the first comment of A257448.
FORMULA
G.f.: -x*(1 + x)*(1 + 10*x + x^2)/((-1 + x)^4*(-1 + 2*x)).
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.
EXAMPLE
This sequence provides the antidiagonal sums of the array:
1, 16, 81, 256, 625, 1296, ... A000583
1, 17, 98, 354, 979, 2275, ... A000538
1, 18, 116, 470, 1449, 3724, ... A101089
1, 19, 135, 605, 2054, 5778, ... A101090
1, 20, 155, 760, 2814, 8592, ... A101091
1, 21, 176, 936, 3750, 12342, ... A254681
...
See also A254681 (Example field).
MATHEMATICA
Table[75 (2^n - 1) - 4 n^3 - 18 n^2 - 52 n, {n, 30}]
PROG
(Magma) [75*(2^n-1)-4*n^3-18*n^2-52*n: n in [1..30]]; // Vincenzo Librandi, Apr 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Apr 23 2015
STATUS
approved