A024014 2^n-n^4.

1, 1, -12, -73, -240, -593, -1232, -2273, -3840, -6049, -8976, -12593, -16640, -20369, -22032, -17857, 0, 47551, 157168, 393967, 888576, 1902671, 3960048, 8108767, 16445440, 33163807, 66651888, 133686287, 267820800, 536163631, 1072931824

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..240

Index entries for linear recurrences with constant coefficients, signature (7,-20,30,-25,11,-2).

Formula

G.f.: (1-6*x+x^2+x^3+26*x^4+x^5) / ((1-2*x)*(1-x)^5). - Vincenzo Librandi, Oct 06 2014

a(n) = 7*a(n-1) -20*a(n-2) +30*a(n-3) -25*a(n-4) +11*a(n-5) -2*a(n-6) for n>5. - Vincenzo Librandi, Oct 06 2014

E.g.f.: exp(2*x) - (x + 7*x^2 + 6*x^3 + x^4)* exp(x). - Robert Israel, Oct 06 2014

Maple

seq(2^n-n^4, n=0..100); # Robert Israel, Oct 06 2014

Mathematica

Table[2^n-n^4, {n, 0, 100}]
CoefficientList[Series[(1 - 6 x + x^2 + x^3 + 26 x^4 + x^5)/((1 - 2 x) (1 - x)^5), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)

Prog

(Magma) [2^n-n^4: n in [0..30]]; // Vincenzo Librandi, Apr 29 2011
(Magma) I:=[1, 1, -12, -73, -240, -593]; [n le 6 select I[n] else 7*Self(n-1)-20*Self(n-2)+30*Self(n-3)-25*Self(n-4)+11*Self(n-5)-2*Self(n-6): n in [1..35]]; // Vincenzo Librandi, Oct 06 2014

Crossrefs

Cf. A024012, A024013.

Cf. sequences of the form k^n-n^4: this sequence (k=2), A024027 (k=3), A024040 (k=4), A024053 (k=5), A024066 (k=6), A024079 (k=7), A024092 (k=8), A024105 (k=9), A024118 (k=10), A024131 (k=11), A024144 (k=12).

Sequence in context: A120793 A120783 A103475 * A069039 A156196 A041270

Adjacent sequences: A024011 A024012 A024013 * A024015 A024016 A024017

Keyword

sign,easy

Author

N. J. A. Sloane.

Status

approved