A393503 Number of paths in the n-necklace graph.

30, 368, 2400, 13056, 65600, 315264, 1471680, 6728192, 30277440, 134567040, 592095680, 2583691008, 11195995200, 48228903296, 206695300800, 881899951104, 3748074793280, 15874199125632, 67024396309440, 282207984462080, 1185273534742080, 4966860526539648

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Graph Path.

Eric Weisstein's World of Mathematics, Necklace Graph.

Index entries for linear recurrences with constant coefficients, signature (10,-33,40,-16).

Formula

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

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

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

Mathematica

Table[(77 4^n - 128) n/6, {n, 20}]
LinearRecurrence[{10, -33, 40, -16}, {30, 368, 2400, 13056}, 20]
CoefficientList[Series[-2 (-15 - 34 x + 145 x^2)/(1 - 5 x + 4 x^2)^2, {x, 0, 20}], x]

Crossrefs

Sequence in context: A058837 A042748 A202074 * A251895 A022690 A224332

Adjacent sequences: A393500 A393501 A393502 * A393504 A393505 A393506

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 17 2026

Status

approved