OFFSET
0,2
COMMENTS
The n-prism graph is defined from n >= 3. The sequence has been extrapolated to n = 0 using the recurrence. - Andrew Howroyd, Jan 26 2023
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
Eric Weisstein's World of Mathematics, Edge Cut
Eric Weisstein's World of Mathematics, Prism Graph
Index entries for linear recurrences with constant coefficients, signature (20, -146, 488, -777, 612, -228, 32).
FORMULA
G.f.: (1 - 16*x + 97*x^2 - 210*x^3 + 84*x^4 + 12*x^5 + 4*x^6)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2). - Andrew Howroyd, Jan 26 2023
a(n) = 20*a(n-1)-146*a(n-2)+488*a(n-3)-777*a(n-4)+612*a(n-5)-228*a(n-6)+32*a(n-7). - Eric W. Weisstein, Dec 01 2024
MATHEMATICA
Table[2 + 8^n + n + (((17^(-1/2) - 1) n - 2) (5 + Sqrt[17])^n - ((17^(-1/2) + 1) n + 2) (5 - Sqrt[17])^n)/2^(n + 1), {n, 0, 20}] // Expand (* Eric W. Weisstein, Dec 01 2024 *)
LinearRecurrence[{20, -146, 488, -777, 612, -228, 32}, {1, 4, 31, 314, 3013, 27060, 232671}, 20] (* Eric W. Weisstein, Dec 01 2024 *)
CoefficientList[Series[-(1 - 16 x + 97 x^2 - 210 x^3 + 84 x^4 + 12 x^5 + 4 x^6)/((-1 + x)^2 (-1 + 8 x) (1 - 5 x + 2 x^2)^2), {x, 0, 20}], x]
PROG
(PARI) Vec((1 - 16*x + 97*x^2 - 210*x^3 + 84*x^4 + 12*x^5 + 4*x^6)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2) + O(x^21)) \\ Andrew Howroyd, Jan 26 2023
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Eric W. Weisstein, Jan 07 2023
EXTENSIONS
a(0)-a(2) prepended and terms a(8) and beyond from Andrew Howroyd, Jan 26 2023
STATUS
approved