OFFSET
1,1
COMMENTS
Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Jun 05 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Graph Path
Index entries for linear recurrences with constant coefficients, signature (10, -37, 64, -58, 36, -26, 16, -5, 2, -1).
FORMULA
From Andrew Howroyd, Jun 05 2017 (Start)
a(n) = 10*a(n-1)-37*a(n-2)+64*a(n-3) -58*a(n-4)+36*a(n-5)-26*a(n-6) +16*a(n-7)-5*a(n-8) +2*a(n-9)-a(n-10) for n>10.
G.f.: 2*x*(2*x^6+4*x^5+x^4+24*x^3-4*x^2+20*x+1) * (1-2*x-x^2) / ((1-x)^4 * (1-3*x-x^2-x^3)^2).
(End)
MATHEMATICA
Table[n RootSum[-1 - # - 3 #^2 + #^3 &, 23 #^n + 32 #^(n + 1) + 5 #^(n + 2) &]/44 - 7 n - 3 n^2 - 2 n^3, {n, 20}]
LinearRecurrence[{10, -37, 64, -58, 36, -26, 16, -5, 2, -1}, {2, 56, 396, 2040, 9130, 37944, 151172, 586608, 2235618, 8407640}, 20]
CoefficientList[Series[(2 (2 x^6 + 4 x^5 + x^4 + 24 x^3 - 4 x^2 + 20 x + 1) (1 - 2 x - x^2))/((1 - x)^4 (1 - 3 x - x^2 - x^3)^2), {x, 0, 20}], x]
PROG
(PARI)
Vec(2*(2*x^6+4*x^5+x^4+24*x^3-4*x^2+20*x+1)*(1-2*x-x^2)/((1-x)^4*(1-3*x-x^2-x^3)^2) + O(x^20)) \\ Andrew Howroyd, Jun 05 2017
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Eric W. Weisstein, Jun 03 2017
EXTENSIONS
a(1)-a(2) and a(14)-a(24) from Andrew Howroyd, Jun 05 2017
STATUS
approved