OFFSET
2,1
COMMENTS
The sequence has been extended to a(2)-a(4) using the formula/recurrence. - Andrew Howroyd, Aug 29 2025
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..1000
Eric Weisstein's World of Mathematics, Flower Graph.
Eric Weisstein's World of Mathematics, Hamiltonian Path.
Index entries for linear recurrences with constant coefficients, signature (4,0,-16,14,8,-16,32,-25,-28,32,-16,12,16,-16).
FORMULA
G.f.: x^2*(48 - 72*x^2 - 236*x^3 + 104*x^4 + 136*x^5 + 48*x^6 + 88*x^7 - 112*x^8 + 304*x^9 - 312*x^10 - 44*x^11 + 56*x^12 - 56*x^13)/((1 - x)*(1 + x)*(1 - 2*x)*(1 + x^2)*(1 - 2*x^2))^2. - Andrew Howroyd, Aug 29 2025
a(n) = 4*a(n-1)-16*a(n-3)+14*a(n-4)+8*a(n-5)-16*a(n-6)+32*a(n-7)-25*a(n-8)-28*a(n-9)+32*a(n-10)-16*a(n-11)+12*a(n-12)+16*a(n-13)-16*a(n-14). - Eric W. Weisstein, Sep 03 2025
MATHEMATICA
Table[I^(3 n) n (4 + 4 (-1)^n + 57 (2 I)^n - 2 (12 + 25 2^(n/2)) Cos[n Pi/2] - 25 I 2^((n + 3)/2) Sin[n Pi/2])/4, {n, 2, 20}] (* Eric W. Weisstein, Sep 03 2025 *)
LinearRecurrence[{4, 0, -16, 14, 8, -16, 32, -25, -28, 32, -16, 12, 16, -16}, {48, 192, 696, 1780, 4824, 11368, 27552, 62064, 141840, 312224, 690768, 1496768, 3246096, 6956160}, 20] (* Eric W. Weisstein, Sep 03 2025 *)
CoefficientList[Series[(48 - 72 x^2 - 236 x^3 + 104 x^4 + 136 x^5 + 48 x^6 + 88 x^7 - 112 x^8 + 304 x^9 - 312 x^10 - 44 x^11 + 56 x^12 - 56 x^13)/((1 - x) (1 + x) (1 - 2 x) (1 + x^2) (1 - 2 x^2))^2, {x, 0, 20}], x] (* Eric W. Weisstein, Sep 03 2025 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 29 2025
EXTENSIONS
a(2)-a(4) prepended and a(16) onwards from Andrew Howroyd, Aug 29 2025
STATUS
approved