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Number of singular points on n-th order Chmutov surface.
1

%I #12 Jan 03 2020 10:40:12

%S 0,1,3,14,28,57,93,154,216,321,425,576,732,949,1155,1450,1728,2097,

%T 2457,2926,3360,3941,4477,5160,5808,6625,7371,8334,9212,10305,11325,

%U 12586,13728,15169,16473,18072,19548,21349,22971,24986,26800,29001

%N Number of singular points on n-th order Chmutov surface.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChmutovSurface.html">Chmutov Surface.</a> [Gives a formula]

%F Appears to satisfy a 13-term linear recurrence. - _Ralf Stephan_, Mar 07 2004

%F Conjectures from _Colin Barker_, Jan 02 2020: (Start)

%F G.f.: x^2*(1 + 3*x + 12*x^2 + 21*x^3 + 27*x^4 + 28*x^5 + 31*x^6 + 25*x^7 + 18*x^8 + 11*x^9 + 3*x^10) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)*(1 + x + x^2)^2).

%F a(n) = 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) + a(n-6) + a(n-7) - 2*a(n-8) - a(n-9) + a(n-10) + 2*a(n-11) - a(n-13) for n>13.

%F (End)

%K nonn

%O 1,3

%A _Eric W. Weisstein_