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A136252 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3). 5
1, 3, 5, 9, 13, 21, 29, 45, 61, 93, 125, 189, 253, 381, 509, 765, 1021, 1533, 2045, 3069, 4093, 6141, 8189, 12285, 16381, 24573, 32765, 49149, 65533, 98301, 131069, 196605, 262141, 393213, 524285, 786429, 1048573, 1572861, 2097149, 3145725, 4194301 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A060482 without the term 2.

For n >= 2, number of n X n arrays with values that are squares of integers, having all 2 X 2 subblocks summing to 4. - R. H. Hardin, Apr 03 2009

Number of moves required in 4-peg Tower of Hanoi solution using a (suboptimal) recursive algorithm: Move (n-2) disks, move bottom 2 disks, move (n-2) disks. Cf. A007664. - Toby Gottfried, Nov 29 2010

Partial sums of A163403.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2).

FORMULA

a(n) = 2^((1/2)*n-1)*(4 + 4(-1)^n + 3*sqrt(2)*(1-(-1)^n)) - 3. - Emeric Deutsch, Mar 31 2008

a(n) = -2*(1 + sqrt(2))^(-1)*a(0)*(1 - sqrt(2))^(-1) - (1/4)*sqrt(2)*sqrt(2)^n*(1 - sqrt(2))^(-1)*a(2) + (1/2)*sqrt(2)^n*a(0)*(1 - sqrt(2))^(-1) + (-4 - 2*sqrt(2))^(-1)*(-sqrt(2))^n*a(1) + (-4 - 2*sqrt(2))^(-1)*sqrt(2)*(-sqrt(2))^n*a(1) - (-4 - 2*sqrt(2))^(-1)*sqrt(2)*(-sqrt(2))^n*a(0) - (1/2)*sqrt(2)^n*a(1)*(1 - sqrt(2))^(-1) + (1 + sqrt(2))^(-1)*(1 - sqrt(2))^(-1)*a(2) - (-4 - 2*sqrt(2))^(-1)*(-sqrt(2))^n*a(2) + (1/4)*sqrt(2)*sqrt(2)^n*a(1)*(1 - sqrt(2))^(-1). - Alexander R. Povolotsky, Mar 31 2008

G.f.: (1+2*x)/((1-x)*(1-2*x^2)). - Jaume Oliver Lafont, Aug 30 2009

a(n) = 2*a(n-2) + 3; first differences are powers of 2, occurring in pairs. - Toby Gottfried, Nov 29 2010

a(n) = A027383(n+1) - 1. - Jason Kimberley, Nov 01 2011

a(2n+1) = (a(2n) + a(2n+2))/2. - Richard R. Forberg, Nov 30 2013

MAPLE

a:=proc(n) options operator, arrow: 2^((1/2)*n-1)*(4+4*(-1)^n+3*sqrt(2)*(1-(-1)^n))-3 end proc: seq(a(n), n=0..40); # Emeric Deutsch, Mar 31 2008

MATHEMATICA

LinearRecurrence[{1, 2, -2}, {1, 3, 5}, 100] (* G. C. Greubel, Feb 18 2017 *)

PROG

(PARI) x='x+O('x^50); Vec((1+2*x)/((1-x)*(1-2*x^2))) \\ G. C. Greubel, Feb 18 2017

CROSSREFS

Same recurrence as in A135530.

Cf. A007664 (Optimal 4-peg Tower of Hanoi).

Sequence in context: A206297 A320596 A227565 * A187212 A141325 A248604

Adjacent sequences:  A136249 A136250 A136251 * A136253 A136254 A136255

KEYWORD

nonn

AUTHOR

Paul Curtz, Mar 17 2008

EXTENSIONS

Edited by N. J. A. Sloane, Apr 18 2008

More terms from Emeric Deutsch, Mar 31 2008

STATUS

approved

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)