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

1,2

Comments

See the first comment of A257448.

Links

Table of n, a(n) for n=1..29.

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

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

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

Sequence in context: A294586 A265838 A098997 * A301548 A337166 A139497

Adjacent sequences: A257446 A257447 A257448 * A257450 A257451 A257452

Keyword

nonn,easy

Author

Luciano Ancora, Apr 23 2015

Status

approved