OFFSET
1,2
COMMENTS
The n-prism graph is well defined for n >= 3. Sequence extended to n = 1 using recurrence. - Andrew Howroyd, Aug 10 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Minimal Edge Cover
Eric Weisstein's World of Mathematics, Prism Graph
Index entries for linear recurrences with constant coefficients, signature (1, 2, 6, 2, 2, -2, -2, -1, 1).
FORMULA
From Andrew Howroyd, Aug 10 2017: (Start)
a(n) = a(n-1) + 2*a(n-2) + 6*a(n-3) + 2*a(n-4) + 2*a(n-5) - 2*a(n-6) - 2*a(n-7) - a(n-8) + a(n-9) for n > 9.
G.f.: x*(1 + 4*x + 18*x^2 + 8*x^3 + 10*x^4 - 12*x^5 - 14*x^6 - 8*x^7 + 9*x^8)/((1 - 2*x - 2*x^2 + x^4)*(1 + x + x^2 - x^3)*(1 + x^2)).
(End)
MATHEMATICA
Table[2 Cos[n Pi/2] + RootSum[-1 + # + #^2 + #^3 &, #^n &] -
RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, -2 #^(n + 2) - 2 #^(n + 3) + #^(n + 4) &], {n, 20}]
LinearRecurrence[{1, 2, 6, 2, 2, -2, -2, -1, 1}, {1, 5, 25, 49, 141, 389, 1009, 2761, 7441}, 20]
CoefficientList[Series[-( (1 + 4 x + 18 x^2 + 8 x^3 + 10 x^4 - 12 x^5 - 14 x^6 - 8 x^7 + 9 x^8)/((1 + x^2) (-1 - x - x^2 + x^3) (1 - 2 x - 2 x^2 + x^4))), {x, 0, 20}], x]
PROG
(PARI)
Vec((1 + 4*x + 18*x^2 + 8*x^3 + 10*x^4 - 12*x^5 - 14*x^6 - 8*x^7 + 9*x^8)/((1 - 2*x - 2*x^2 + x^4)*(1 + x + x^2 - x^3)*(1 + x^2))+O(x^30)) \\ Andrew Howroyd, Aug 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 09 2017
EXTENSIONS
a(1)-a(2) and terms a(9) and beyond from Andrew Howroyd, Aug 10 2017
STATUS
approved