A132753 a(n) = 2^(n+1) - n + 1.

3, 4, 7, 14, 29, 60, 123, 250, 505, 1016, 2039, 4086, 8181, 16372, 32755, 65522, 131057, 262128, 524271, 1048558, 2097133, 4194284, 8388587, 16777194, 33554409, 67108840, 134217703, 268435430, 536870885, 1073741796, 2147483619

Offset: 0

Author

Gary W. Adamson, Aug 28 2007

Keywords

• nonn
• easy

Comments

Apart from a(0): Row sums of triangle A132752 (old name).

Apart from a(0): Binomial transform of [1, 3, 0, 4, 0, 4, 0, 4, ...].

Examples

			a(3) = 14 = sum of row 3 terms of triangle A132752: (3 + 5 + 5 + 1).
a(3) = 14 = (1, 3, 3, 1) dot (1, 3, 0, 4) = (1 + 9 + 0 + 4).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A132752.

Cf. A003462, A007051, A024023, A029858, A034472, A052548, A058481, A067771, A079004, A100774, A115099, A134931. - Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Programs

Magma

[2^(n+1) -n+1: n in [0..40]]; // G. C. Greubel, Feb 16 2021

Maple

A132753:= n-> 2^(n+1) -n+1; seq(A132753(n), n=0..40) # G. C. Greubel, Feb 16 2021

Mathematica

Table[2^(n+1) -n+1, {n, 0, 30}] (* Bruno Berselli, Aug 31 2013 *)

PARI

a(n)=2^(n+1)-n+1

PARI

Vec( (3-8*x+6*x^2)/((1-x)^2*(1-2*x)) + O(x^40)) \\ Colin Barker, Mar 14 2014

Sage

[2^(n+1) -n+1 for n in (0..40)] # G. C. Greubel, Feb 16 2021

Formula

From Colin Barker, Mar 14 2014: (Start)

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

G.f.: (3 - 8*x + 6*x^2)/((1-x)^2 * (1-2*x)). (End)

E.g.f.: (1-x)*exp(x) + 2*exp(2*x). - G. C. Greubel, Feb 16 2021

Extensions

More terms Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Changed first member, and better name from Ralf Stephan, Aug 31 2013