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A274845
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a(0)=1, a(1)=0, a(4n+2) = a(4n+3) = a(4n+5) = (4^(n+1) +(-1)^n)/5, a(4n+4) = (2*4^(n+1) -3*(-1)^n)/5.
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1
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1, 0, 1, 1, 1, 1, 3, 3, 7, 3, 13, 13, 25, 13, 51, 51, 103, 51, 205, 205, 409, 205, 819, 819, 1639, 819, 3277, 3277, 6553, 3277, 13107, 13107, 26215, 13107, 52429, 52429, 104857, 52429, 209715, 209715, 419431, 209715, 838861, 838861, 1677721, 838861, 3355443
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OFFSET
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0,7
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COMMENTS
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Antidiagonals of the array in A274613 written as a triangle:
1,
0, 1/2,
0, 1/2, 1/4,
0, 0, 1/2, 1/8,
0, 0, 1/4, 3/8, 1/16,
... .
a(n) is the numerators of the antidiagonal sums i.e. 1, 0, 1/2, 1/2, 1/4, 1/2, 3/8, 3/8, 7/16, 3/8, 13/32, 13/32, 25/64, 13/32, ... = a(n)/b(n).
The denominators b(n) are A173300(n).
a(0)+a(1) = 1, a(4n+2) +a(4n+3) +a(4n+4) +a(4n+5) = 4, 16, 64, 256, ... .
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LINKS
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FORMULA
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G.f.: (1+x^2+x^3-2*x^4+x^5) / ((1-2*x^2)*(1+2*x^2)*(1+x^4)). - Colin Barker, Jul 22 2016
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, 4}, {1, 0, 1, 1, 1, 1, 3, 3}, 50] (* G. C. Greubel, Jul 08 2016 *)
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PROG
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(PARI) Vec((1+x^2+x^3-2*x^4+x^5)/((1-2*x^2)*(1+2*x^2)*(1+x^4)) + O(x^60)) \\ Colin Barker, Jul 22 2016
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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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EXTENSIONS
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STATUS
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approved
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