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A191370
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a(n) = 2*(1+(-1)^n)/3 + 2*A010892(n-1).
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1
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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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n+3) = 3*2^n - a(n), n >= 0.
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
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MAPLE
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A010892 := proc(n) op( 1+(n mod 6), [1, 1, 0, -1, -1, 0]) ; end proc:
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MATHEMATICA
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LinearRecurrence[{2, 0, -1, 2}, {1, 2, 4, 2}, 30] (* Harvey P. Dale, Sep 06 2022 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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