OFFSET
1,2
COMMENTS
Extended to a(1)-a(2) using the formula/recurrence.
For n > 2, also the number of minimal edge cuts in the n-prism graph. - Eric W. Weisstein, Jan 07 2023
LINKS
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Minimal Edge Cut
Eric Weisstein's World of Mathematics, Prism Graph
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
FORMULA
a(n) = n*(n - 1)*(2*n^2 - 4*n + 15)/6 + 1.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x (-1 - x - 2*x^2 - 3*x^3 - x^4)/(-1 + x)^5.
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 6, 22, 63, 151}, 20]
Table[n (n - 1) (2 n^2 - 4 n + 15)/6 + 1, {n, 20}]
CoefficientList[Series[(-1 - x - 2 x^2 - 3 x^3 - x^4)/(-1 + x)^5, {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 19 2019
STATUS
approved