A338336 - OEIS

%I #8 Nov 15 2020 13:12:02

%S 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,

%T 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,

%U 15,15,16,16,17,17,18,18,18,19,18,20,19,21,20,22,21,23,22

%N 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.

%C 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.

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

%H Herbert Kociemba, <a href="http://kociemba.org/themen/kaleidocycles/intro.html">Kaleidocycles with 6 Disphenoids</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaleidocycle">Kaleidocycle</a>

%t 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

%t 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];

%t Array[a,80]

%Y Cf. A338334, A338335.

%K nonn

%O 1,11

%A _Herbert Kociemba_, Oct 22 2020