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

0,1

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, ...].

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).

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

Example

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).

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 *)

Prog

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

Crossrefs

Cf. A132752.

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

Sequence in context: A095063 A003242 A073728 * A132407 A070035 A219277

Adjacent sequences: A132750 A132751 A132752 * A132754 A132755 A132756

Keyword

nonn,easy

Author

Gary W. Adamson, Aug 28 2007

Extensions

More terms Vladimir Joseph Stephan Orlovsky, Dec 25 2008

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

Status

approved