A024022 a(n) = 2^n - n^12.

1, 1, -4092, -531433, -16777200, -244140593, -2176782272, -13841287073, -68719476480, -282429535969, -999999998976, -3138428374673, -8916100444160, -23298085114289, -56693912358912, -129746337857857, -281474976645120

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..230

Index entries for linear recurrences with constant coefficients, signature (15, -104, 442, -1287, 2717, -4290, 5148, -4719, 3289, -1716, 650, -169, 27, -2).

Formula

From Chai Wah Wu, Jan 26 2020: (Start)

a(n) = 15*a(n-1) - 104*a(n-2) + 442*a(n-3) - 1287*a(n-4) + 2717*a(n-5) - 4290*a(n-6) + 5148*a(n-7) - 4719*a(n-8) + 3289*a(n-9) - 1716*a(n-10) + 650*a(n-11) - 169*a(n-12) + 27*a(n-13) - 2*a(n-14) for n > 13.

G.f.: (x^13 + 8178*x^12 + 952381*x^11 + 19897385*x^10 + 122448548*x^9 + 258707385*x^8 + 162510570*x^7 - 29873622*x^6 - 45944391*x^5 - 9230428*x^4 - 470391*x^3 - 4003*x^2 - 14*x + 1)/((x - 1)^13*(2*x - 1)). (End)

Mathematica

CoefficientList[Series[(x^13+8178x^12+952381x^11+19897385x^10+122448548x^9+258707385x^8+162510570x^7-29873622x^6-45944391x^5-9230428x^4-470391x^3-4003x^2-14x+1)/((x-1)^13(2x-1)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -104, 442, -1287, 2717, -4290, 5148, -4719, 3289, -1716, 650, -169, 27, -2}, {1, 1, -4092, -531433, -16777200, -244140593, -2176782272, -13841287073, -68719476480, -282429535969, -999999998976, -3138428374673, -8916100444160, -23298085114289}, 30] (* Harvey P. Dale, Dec 11 2022 *)

Prog

(Magma) [2^n-n^12: n in [0..30] ]; // Vincenzo Librandi, Apr 30 2011

Crossrefs

Sequence in context: A256028 A063889 A257824 * A145591 A103289 A038463

Adjacent sequences: A024019 A024020 A024021 * A024023 A024024 A024025

Keyword

sign

Author

N. J. A. Sloane

Status

approved