A377641 a(n) = 3^n + 2^(3*n + 1) - 2^(2*n + 1).

11, 105, 923, 7761, 63731, 516825, 4163723, 33429921, 267930851, 2145445545, 17171657723, 137405930481, 1099379004371, 8795560934265, 70366611042923, 562941406533441, 4503565396772291, 36028659967430985, 288229827558159323, 2305840813677222801

Offset

1,1

Comments

Also number of edge cuts in the n-book graph.

Links

Table of n, a(n) for n=1..20.

Eric Weisstein's World of Mathematics, Book Graph.

Eric Weisstein's World of Mathematics, Edge Cut.

Index entries for linear recurrences with constant coefficients, signature (15,-68,96).

Formula

a(n) = 15*a(n-1)-68*a(n-2)+96*a(n-3).

G.f.: x*(-11+60*x-96*x^2)/(-1+15*x-68*x^2+96*x^3).

Mathematica

Table[3^n + 2^(3 n + 1) - 2^(2 n + 1), {n, 20}]
LinearRecurrence[{15, -68, 96}, {11, 105, 923}, 20]
CoefficientList[Series[-(11 - 60 x + 96 x^2)/((-1 + 3 x) (-1 + 4 x) (-1 + 8 x)), {x, 0, 20}], x]

Prog

(Python)
def A377641(n): return 3**n+(2<<3*n)-(2<<(n<<1)) # Chai Wah Wu, Nov 03 2024

Crossrefs

Sequence in context: A372146 A163933 A359987 * A099839 A287834 A075183

Adjacent sequences: A377638 A377639 A377640 * A377642 A377643 A377644

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 03 2024

Status

approved