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A191370 a(n) = 2*(1+(-1)^n)/3 + 2*A010892(n-1). 1
1, 2, 4, 2, 4, 8, 22, 44, 88, 170, 340, 680, 1366, 2732, 5464, 10922, 21844, 43688, 87382, 174764, 349528, 699050, 1398100, 2796200, 5592406, 11184812, 22369624, 44739242 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) and successive differences define an infinite array:

    1,   2,   4,   2,   4,   8, ...

    1,   2,  -2,   2,   4,  14, ...

    1,  -4,   4,   2,  10,   8, ...

   -5,   8,  -2,   8,  -2,  14, ...

   13, -10,  10, -10,  16,   2, ...

  -23,  20, -20,  26, -14,  32, ...

  ...

Its main diagonal consists of the powers 2^n. The first upper diagonal is a signed sequence of 2's. The second upper diagonal contains essentially A135440.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

FORMULA

a(n+3) = 3*2^n - a(n), n >= 0.

a(n+1) - 2*a(n) = -6*A131531(n+1).

a(3*n) = A007613(n), a(1+3*n) = 2*A007613(n), a(2+3*n) = 4*A007613(n).

a(n+6) = a(n) + 21*2^n.

a(n) = ((2^n + 2*(-1)^n)*2^n - 2*i*sqrt(3)*((1+i*sqrt(3))^n - (1-i*sqrt(3))^n))/(3*2^n), where i=sqrt(-1); a(n+1) = 2*(A001045(n) + A010892(n)). - Bruno Berselli, Jun 06 2011

G.f.: ( -1+5*x^3 ) / ( (2*x-1)*(1+x)*(x^2-x+1) ). - R. J. Mathar, Jun 06 2011

a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). - Paul Curtz, Jun 07 2011

a(n) = A113405(n+3) - 5*A113405(n). - R. J. Mathar, Jun 24 2011

MAPLE

A010892 := proc(n) op( 1+(n mod 6), [1, 1, 0, -1, -1, 0]) ; end proc:

A191370 := proc(n) 2^n/3+2*(-1)^n/3+2*A010892(n-1) ; end proc:

seq(A191370(n), n=0..30) ; # R. J. Mathar, Jun 06 2011

CROSSREFS

Cf. A010892, A131531, A007613, A001045.

Cf. A007283, A024495, A113405.

Sequence in context: A286557 A278219 A155682 * A298242 A282283 A288416

Adjacent sequences:  A191367 A191368 A191369 * A191371 A191372 A191373

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jun 01 2011

STATUS

approved

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Last modified August 25 10:10 EDT 2019. Contains 326324 sequences. (Running on oeis4.)