

A102762


Curvatures of (largest) kissing circles along the circumference, starting with curvature = 1 and 2.


1



1, 2, 2, 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, 1602, 1683, 1766, 1851, 1938, 2027, 2118, 2211, 2306, 2403, 2502, 2603, 2706, 2811, 2918, 3027, 3138, 3251, 3366
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OFFSET

0,2


COMMENTS

A059100 has a totally different description but is the same sequence (omitting the first two numbers here)


LINKS



FORMULA

a(n) = a(1) + a(2) + a(n1) + 2*sqrt(a(1)*a(2) + a(1)*a(n1) + a(2)*a(n1)) = 1 + a(n1) + 2*(sqrt(2 + a(n1))). (Descartes' curvaturetheorem)
a(n) = n^2  4*n + 6 for n > 1.
a(n) = 3*a(n1)  3*a(n2) + a(n3) for n > 4.
G.f.: (x^4 + 4*x^3  7*x^2 + 5*x  1)/(x  1)^3.
(End)


PROG

(PARI) a(n) = if(n>1, n^2  4*n + 6, [1, 2][n+1]) \\ Andrew Howroyd, Feb 25 2018


CROSSREFS



KEYWORD

sign,easy


AUTHOR



STATUS

approved



