A393503 - OEIS

%I #4 Feb 17 2026 15:19:34

%S 30,368,2400,13056,65600,315264,1471680,6728192,30277440,134567040,

%T 592095680,2583691008,11195995200,48228903296,206695300800,

%U 881899951104,3748074793280,15874199125632,67024396309440,282207984462080,1185273534742080,4966860526539648

%N Number of paths in the n-necklace graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NecklaceGraph.html">Necklace Graph</a>.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-33,40,-16).

%F a(n) = (77*4^n - 128)*n/6.

%F a(n) = 10*a(n-1)-33*a(n-2)+40*a(n-3)-16*a(n-4).

%F G.f.: -2*x*(-15-34*x+145*x^2)/(1-5*x+4*x^2)^2.

%t Table[(77 4^n - 128) n/6, {n, 20}]

%t LinearRecurrence[{10, -33, 40, -16}, {30, 368, 2400, 13056}, 20]

%t CoefficientList[Series[-2 (-15 - 34 x + 145 x^2)/(1 - 5 x + 4 x^2)^2, {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Feb 17 2026