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

Author

Barry E. Williams, Jan 17 2000

Keywords

• sign
• easy

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).

Crossrefs

Cf. A023444.

Cf. A027992, A048496.

Programs

GAP

List([0..30], n-> 2^(n-1)*(3*n-4)) # G. C. Greubel, May 16 2019

Magma

[2^(n-1)*(3*n-4): n in [0..30]]; // Vincenzo Librandi, Sep 26 2011

Mathematica

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

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

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