OFFSET
0,2
COMMENTS
The sequence has been extended to n = 0 using the recurrence. - Andrew Howroyd, Dec 19 2024
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, Trapezohedral Graph.
Index entries for linear recurrences with constant coefficients, signature (39,-531,2997,-6588,5956,-2128,256).
FORMULA
G.f.: (1 - 26*x + 209*x^2 - 296*x^3 - 636*x^4 + 248*x^5 + 80*x^6)/((1 - x)*(1 - 16*x)*(1 - 12*x + 4*x^2)*(1 - 10*x + 17*x^2 - 4*x^3)). - Andrew Howroyd, Dec 19 2024
a(n) = 39*a(n-1)-531*a(n-2)+2997*a(n-3)-6588*a(n-4)+5956*a(n-5)-2128*a(n-6)+256*a(n-7). - Eric W. Weisstein, Sep 06 2025
MATHEMATICA
Table[16^n - 1 - 2^(n + 1) ChebyshevT[n, 3] + RootSum[-4 + 17 # - 10 #^2 + #^3 &, #^n &], {n, 0, 20}] (* Eric W. Weisstein, Sep 06 2025 *)
LinearRecurrence[{39, -531, 2997, -6588, 5956, -2128, 256}, {3013, 51009, 864453, 14514449, 241137749, 3969473217, 64867543333}, {-2, 20}] (* Eric W. Weisstein, Sep 06 2025 *)
CoefficientList[Series[-(1 - 26 x + 209 x^2 - 296 x^3 - 636 x^4 + 248 x^5 + 80 x^6)/((-1 + x) (-1 + 16 x) (1 - 12 x + 4 x^2) (-1 + 10 x - 17 x^2 + 4 x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 06 2025 *)
PROG
(PARI) Vec((1 - 26*x + 209*x^2 - 296*x^3 - 636*x^4 + 248*x^5 + 80*x^6)/((1 - x)*(1 - 16*x)*(1 - 12*x + 4*x^2)*(1 - 10*x + 17*x^2 - 4*x^3)) + O(x^21)) \\ Andrew Howroyd, Dec 19 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Nov 06 2024
EXTENSIONS
a(0)-a(2) prepended and a(7) onwards from Andrew Howroyd, Dec 19 2024
STATUS
approved