A140657 Powers of 2 with 3 alternatingly added and subtracted.

4, -1, 7, 5, 19, 29, 67, 125, 259, 509, 1027, 2045, 4099, 8189, 16387, 32765, 65539, 131069, 262147, 524285, 1048579, 2097149, 4194307, 8388605, 16777219, 33554429, 67108867, 134217725, 268435459, 536870909, 1073741827, 2147483645, 4294967299, 8589934589

Offset: 0

Author

Paul Curtz, Jul 10 2008

Keywords

• sign
• easy

Links

• Jean-François Alcover and Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (first 101 terms from Jean-François Alcover)
• Index entries for linear recurrences with constant coefficients, signature (1, 2).

Crossrefs

Cf. A000079, A007283, A010734, A033999, A096045, A140683.

Programs

Magma

[2^n+3*(-1)^n: n in [0..40]]; // Vincenzo Librandi, Aug 08 2011

Mathematica

LinearRecurrence[{1,2},{4,-1},40] (* or *) Total/@Partition[Riffle[ Table[ 2^n, {n,0,40}],{3,-3}],2] (* Harvey P. Dale, Nov 13 2014 *)
CoefficientList[Series[(4 - 5 x) / ((1 + x) (1 - 2 x)), {x, 0, 50}], x] (* Vincenzo Librandi, Jan 14 2015 *)

Formula

a(2n) = A000079(2n+1) + 3, a(2n+1) = A000079(2n+2) - 3.

a(n+1) - 2*a(n) = -9*A033999(n) = (-1)^(n+1)*A010734.

a(n) + a(n+1) = 3^*2^n = A007283(n).

a(2n) + a(2n+1) = A096045(n) + 2.

a(-n) = -A140683(n)/2^n.

O.g.f.: (4-5*x)/((1-2*x)(1+x)). - R. J. Mathar, Jul 29 2008

a(n) = 2^n+3*(-1)^n. - R. J. Mathar , Jul 29 2008

Extensions

Edited and extended by R. J. Mathar, Jul 29 2008

4 inserted as first term and formulas accordingly updated by Jean-François Alcover, Jan 14 2015