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A132753 2^(n+1) - n + 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

FORMULA

a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3). G.f.: -(6*x^2-8*x+3) / ((x-1)^2*(2*x-1)). - Colin Barker, Mar 14 2014

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).

MATHEMATICA

a = 3; lst = {3}; Do[a = a*2 + n - 3; AppendTo[lst, a], {n, 1, 30}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 25 2008 *)

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(-(6*x^2-8*x+3)/((x-1)^2*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 14 2014

CROSSREFS

Cf. A132752.

Cf. A003462, A007051, A034472, A024023, A067771, A029858, A134931, A115099, A100774, A079004, A058481, A052548. - 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

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)