A387457 Number of Hamiltonian paths in the n-Goldberg graph.

2772, 13096, 43400, 142680, 413168, 1162304, 3080736, 7966880, 19932352, 48943488, 117719680, 279180160, 652834560, 1510279168, 3458421248, 7853658624, 17697041408, 39614228480, 88136509440, 195043481600, 429506424832, 941650132992, 2056105369600, 4472971829248

Offset

3,1

Links

Andrew Howroyd, Table of n, a(n) for n = 3..1000

Eric Weisstein's World of Mathematics, Goldberg Graph.

Eric Weisstein's World of Mathematics, Hamiltonian Path.

Index entries for linear recurrences with constant coefficients, signature (6,-8,-16,44,-8,-48,32).

Formula

G.f.: x^3*(2772 - 3536*x - 13000*x^2 + 31400*x^3 - 8144*x^4 - 34912*x^5 + 23360*x^6 + 768*x^7)/((1 - 2*x)^3*(1 - 2*x^2)^2). - Andrew Howroyd, Aug 29 2025

a(n) = 6*a(n-1)-8*a(n-2)-16*a(n-3)+44*a(n-4)-8*a(n-5)-48*a(n-6)+32*a(n-7) for n > 8. - Eric W. Weisstein, Sep 03 2025

Mathematica

Join[{2772}, Table[2^((n - 5)/2) (1124 (1 - (-1)^n) + 929 Sqrt[2] (1 + (-1)^n)) n + 3 2^(n - 1) n (75 n - 241), {n, 4, 20}]] // Expand
Join[{2772}, LinearRecurrence[{6, -8, -16, 44, -8, -48, 32}, {13096, 43400, 142680, 413168, 1162304, 3080736, 7966880}, 20]]
CoefficientList[Series[-4 (693 - 884 x - 3250 x^2 + 7850 x^3 - 2036 x^4 - 8728 x^5 + 5840 x^6 + 192 x^7)/((-1 + 2 x)^3 (-1 + 2 x^2)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A046380 A249228 A154081 * A362876 A099691 A231739

Adjacent sequences: A387454 A387455 A387456 * A387458 A387459 A387460

Keyword

nonn

Author

Eric W. Weisstein, Aug 29 2025

Extensions

a(8) onwards from Andrew Howroyd, Aug 29 2025

Status

approved