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A338336 Number of integer-sided disphenoids (isosceles tetrahedra) with triangle face perimeter n which can be used to build a kaleidocycle by connecting 6 congruent pieces into a cycle. 2
0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 6, 5, 6, 6, 7, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 9, 11, 10, 11, 11, 12, 11, 12, 12, 14, 13, 14, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 18, 19, 18, 20, 19, 21, 20, 22, 21, 23, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

Three positive numbers a, b and c (without loss of generality c<=a, c<=b) define the faces of a disphenoid which can be used for a kaleidocycle if and only if -8*(a^2-b^2)^2*(a^2+b^2)-5*c^6+11*(a^2-b^2)^2*c^2+2*(a^2+b^2)*c^4>=0.

REFERENCES

Doris Schattschneider and Wallace Walker, M.C. Escher Kaleidocycles, 1977. ISBN 0-906212-28-6

LINKS

Table of n, a(n) for n=1..80.

Herbert Kociemba, Kaleidocycles with 6 Disphenoids

Wikipedia, Kaleidocycle

MATHEMATICA

value[a_, b_, c_]:=-8 (a^2-b^2)^2 (a^2+b^2)-5 c^6+11 (a^2-b^2)^2 c^2+2 (a^2+b^2) c^4

a[n_]:=Module[{a, b, c, t=0}, Do[If[a=n-b-c; a>=b&&value[a, b, c]>=0, t++], {c, Quotient[n, 3]}, {b, c, n-c}]; t];

Array[a, 80]

CROSSREFS

Cf. A338334, A338335.

Sequence in context: A026806 A261348 A320536 * A298783 A053280 A289122

Adjacent sequences:  A338333 A338334 A338335 * A338337 A338338 A338339

KEYWORD

nonn

AUTHOR

Herbert Kociemba, Oct 22 2020

STATUS

approved

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Last modified June 21 03:17 EDT 2021. Contains 345354 sequences. (Running on oeis4.)