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A329774
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a(n) = n+1 for n <= 2; otherwise a(n) = 3*a(n-3)+1.
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3
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1, 2, 3, 4, 7, 10, 13, 22, 31, 40, 67, 94, 121, 202, 283, 364, 607, 850, 1093, 1822, 2551, 3280, 5467, 7654, 9841, 16402, 22963, 29524, 49207, 68890, 88573, 147622, 206671, 265720, 442867, 620014, 797161, 1328602, 1860043, 2391484, 3985807
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OFFSET
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0,2
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COMMENTS
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Robert Fathauer observed that if the "warp and woof" construction used by Jim Conant in his recursive dissection of a square (see A328078) is applied to a triangle, one obtains the Sierpinski gasket.
The present sequence gives the number of regions after the n-th generation of this dissection of a triangle.
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REFERENCES
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Robert Fathauer, Email to N. J. A. Sloane, Oct 14 2019.
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LINKS
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FORMULA
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G.f.: (1 + x + x^2 - 2*x^3) / ((1 - x)*(1 - 3*x^3)).
a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) for n>3.
(End)
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MAPLE
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f:=proc(n) option remember;
if n<=2 then n+1 else 3*f(n-3)+1; fi; end;
[seq(f(n), n=0..50)];
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PROG
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(PARI) Vec((1 + x + x^2 - 2*x^3) / ((1 - x)*(1 - 3*x^3)) + O(x^40)) \\ Colin Barker, Nov 27 2019
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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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