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Search: id:A064412
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| A064412 |
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At stage 1, start with a unit equilateral equiangular triangle. At each successive stage add 3*(n-1) new triangles around outside with edge-to-edge contacts. Sequence gives number of triangles (regardless of size) at n-th stage. |
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+0
2
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| 1, 5, 14, 32, 60, 103, 160, 238, 335, 459, 606, 786, 994, 1241, 1520, 1844, 2205, 2617, 3070, 3580, 4136, 4755, 5424, 6162, 6955, 7823, 8750, 9758, 10830, 11989, 13216, 14536, 15929, 17421, 18990, 20664, 22420, 24287, 26240, 28310, 30471
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of unit triangles at n-th stage = 3n(n-1)/2 + 1, A005448.
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REFERENCES
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Anthony Gardiner, "Mathematical Puzzling," Dover Publications, Inc., Mineola, NY., 1987, page 88.
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FORMULA
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a(2n+1) = (7n^3+12n^2+7n+2)/2; a(2n) = (28n^3+6n^2+4n+1+(-1)^(n+1))/8. - Len Smiley (smiley(AT)math.uaa.alaska.edu), Oct 07 2001
G.f.: (1+x+x^2)(1+2x+x^2+3x^3)/((1-x)^2(1-x^2)(1-x^4)).
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EXAMPLE
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a(4) = 32: 19 triangles of side 1, 10 of side 2 and 3 of side 3.
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PROGRAM
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(PARI) a(n)=polcoeff(x*(1+x+x^2)*(1+2*x+x^2+3*x^3)/((1-x)^2*(1-x^2)*(1-x^4))+x*O(x^n), n)
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CROSSREFS
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Cf. A056640.
Adjacent sequences: A064409 A064410 A064411 this_sequence A064413 A064414 A064415
Sequence in context: A023652 A101648 A070134 this_sequence A036595 A053209 A014302
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 29 2001
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EXTENSIONS
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More terms from Len Smiley (smiley(AT)math.uaa.alaska.edu), Oct 07 2001
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