A257449 a(n) = 75*(2^n - 1) - 4*n^3 - 18*n^2 - 52*n.

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

Author

Luciano Ancora, Apr 23 2015

Keywords

• nonn
• easy

Comments

See the first comment of A257448.

Examples

			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).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

Crossrefs

Cf. A000225, A000670, A050488, A208744, A257448, A257450.

Programs

Magma

[75*(2^n-1)-4*n^3-18*n^2-52*n: n in [1..30]]; // Vincenzo Librandi, Apr 24 2015

Mathematica

Table[75 (2^n - 1) - 4 n^3 - 18 n^2 - 52 n, {n, 30}]

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.