A053565 a(n) = 2^(n-1)*(3*n-4).

-2, -1, 4, 20, 64, 176, 448, 1088, 2560, 5888, 13312, 29696, 65536, 143360, 311296, 671744, 1441792, 3080192, 6553600, 13893632, 29360128, 61865984, 130023424, 272629760, 570425344, 1191182336, 2483027968, 5167382528, 10737418240

Offset

0,1

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (4,-4).

Formula

a(n) = 4*a(n-1) - 4*a(n-2), with a(0) = -2, a(1) = -1.

G.f.: -(2-7*x)/(1-2*x)^2. - Colin Barker, Apr 07 2012

E.g.f.: (3*x - 2)*exp(2*x). - G. C. Greubel, May 16 2019

Mathematica

Table[2^(n-1)*(3*n-4), {n, 0, 30}] (* G. C. Greubel, May 16 2019 *)

Prog

(Magma) [2^(n-1)*(3*n-4): n in [0..30]]; // Vincenzo Librandi, Sep 26 2011
(PARI) vector(30, n, n--; 2^(n-1)*(3*n-4)) \\ G. C. Greubel, May 16 2019
(Sage) [2^(n-1)*(3*n-4) for n in (0..30)] # G. C. Greubel, May 16 2019
(GAP) List([0..30], n-> 2^(n-1)*(3*n-4)) # G. C. Greubel, May 16 2019

Crossrefs

Cf. A023444.

Cf. A027992, A048496.

Sequence in context: A032105 A259472 A354055 * A116603 A354056 A158356

Adjacent sequences: A053562 A053563 A053564 * A053566 A053567 A053568

Keyword

sign,easy

Author

Barry E. Williams, Jan 17 2000

Status

approved