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Search: id:A067628
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| A067628 |
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Minimal perimeter of polyiamond with n triangles. |
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+0
6
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| 0, 3, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 12, 11, 12, 13, 12, 13, 12, 13, 14, 13, 14, 15, 14, 15, 14, 15, 16, 15, 16, 15, 16, 17, 16, 17, 16, 17, 18, 17, 18, 17, 18, 19, 18, 19, 18, 19, 18, 19, 20, 19, 20, 19, 20, 21, 20, 21, 20, 21, 20, 21, 22, 21, 22, 21, 22
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A polyiamond is a shape made up of n congruent equilateral triangles.
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REFERENCES
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J. Yackel, R. R. Meyer, I. Christou, Minimum-perimeter domain assignment, Mathematical Programming, vol. 78 (1997), pp. 283-303
W. C. Yang and R. R. Meyer, Maximal and minimal polyiamonds, manuscript, 2002.
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FORMULA
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Let c(n) = ceil(sqrt(6n)). Then a(n) is whichever of c(n) or c(n) + 1 has the same parity as n.
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MAPLE
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interface(quiet=true); for n from 0 to 100 do if (1 = 1) then temp1 := ceil(sqrt(6*n)); end if; if ((temp1 mod 2) = (n mod 2)) then temp2 := 0; else temp2 := 1; end if; printf("%d, ", temp1 + temp2); od;
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CROSSREFS
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Cf. A000577, A000105, A057729, A027709 (squares), A065777 (cubes).
Cf. A135711.
Sequence in context: A049267 A111608 A126800 this_sequence A095254 A121857 A121854
Adjacent sequences: A067625 A067626 A067627 this_sequence A067629 A067630 A067631
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KEYWORD
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nonn
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AUTHOR
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Winston C. Yang (winston(AT)cs.wisc.edu), Feb 02 2002
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