A024016 2^n-n^6.

1, 1, -60, -721, -4080, -15593, -46592, -117521, -261888, -530929, -998976, -1769513, -2981888, -4818617, -7513152, -11357857, -16711680, -24006497, -33750080, -46521593, -62951424, -83668969, -109185600, -139647281, -174325760, -210586193, -241806912

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..239

Index entries for linear recurrences with constant coefficients, signature (9,-35,77,-105,91,-49,15,-2).

Formula

G.f.: (1-8*x-34*x^2-223*x^3+337*x^4+526*x^5+120*x^6+x^7) / ((1-2* x)*(1-x)^7). - Vincenzo Librandi, Oct 07 2014

a(n) = 9*a(n-1) -35*a(n-2) +77*a(n-3) -105*a(n-4) +91*a(n-5) -49*a(n-6) +15*a(n-7) -2*a(n-8) for n>7. - Vincenzo Librandi, Oct 07 2014

Mathematica

Table[2^n - n^6, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 8 x - 34 x^2 - 223 x^3 + 337 x^4 + 526 x^5 + 120 x^6 + x^7)/((1 - 2 x) (1 - x)^7), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 07 2014 *)
LinearRecurrence[{9, -35, 77, -105, 91, -49, 15, -2}, {1, 1, -60, -721, -4080, -15593, -46592, -117521}, 30] (* Harvey P. Dale, Oct 04 2019 *)

Prog

(Magma) [2^n-n^6: n in [0..25]]; // Vincenzo Librandi, Apr 30 2011
(Magma) I:=[1, 1, -60, -721, -4080, -15593, -46592, -117521]; [n le 8 select I[n] else 9*Self(n-1)-35*Self(n-2)+77*Self(n-3)-105*Self(n-4)+91*Self(n-5)-49*Self(n-6)+15*Self(n-7)-2*Self(n-8): n in [1..35]]; // Vincenzo Librandi, Oct 07 2014

Crossrefs

Cf. sequences of the form k^n-n^6: this sequence (k=2), A024029 (k=3), A024042 (k=4), A024055 (k=5), A024068 (k=6), A024081 (k=7), A024094 (k=8), A024107 (k=9), A024120 (k=10), A024133 (k=11), A024146 (k=12).

Sequence in context: A000555 A034865 A138409 * A348583 A349871 A112042

Adjacent sequences: A024013 A024014 A024015 * A024017 A024018 A024019

Keyword

sign,easy

Author

N. J. A. Sloane.

Status

approved