A057870 Number of singular points on n-th order Chmutov surface.

0, 1, 3, 14, 28, 57, 93, 154, 216, 321, 425, 576, 732, 949, 1155, 1450, 1728, 2097, 2457, 2926, 3360, 3941, 4477, 5160, 5808, 6625, 7371, 8334, 9212, 10305, 11325, 12586, 13728, 15169, 16473, 18072, 19548, 21349, 22971, 24986, 26800, 29001

Offset

1,3

Links

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Chmutov Surface. [Gives a formula]

Formula

Appears to satisfy a 13-term linear recurrence. - Ralf Stephan, Mar 07 2004

Conjectures from Colin Barker, Jan 02 2020: (Start)

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).

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.

(End)

Crossrefs

Sequence in context: A032041 A031002 A085762 * A256053 A354041 A031049

Adjacent sequences: A057867 A057868 A057869 * A057871 A057872 A057873

Keyword

nonn

Author

Eric W. Weisstein

Status

approved