A362526 a(n) = 2^n*(n + 2) + (n - 7)*n/2 - 2.

1, 9, 32, 88, 217, 507, 1150, 2562, 5639, 12301, 26644, 57372, 122917, 262191, 557114, 1179718, 2490451, 5242977, 11010160, 23068800, 48234641, 100663459, 209715382, 436207818, 905969887, 1879048437, 3892314380, 8053063972, 16642998589, 34359738711

Offset

1,2

Comments

For n > 2, number of vertex cuts in the n-crown graph.

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Crown Graph

Eric Weisstein's World of Mathematics, Vertex Cut

Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).

Formula

a(n) = 7*a(n-1)-19*a(n-2)+25*a(n-3)-16*a(n-4)+4*a(n-5).

G.f.: -x*(1 + 2*x - 12*x^2 + 10*x^3)/((-1 + x)^3*(-1 + 2*x)^2).

Mathematica

Table[2^n (n + 2) + (n - 7) n /2 - 2, {n, 20}]
LinearRecurrence[{7, -19, 25, -16, 4}, {1, 9, 32, 88, 217}, 20]
CoefficientList[Series[-(1 + 2 x - 12 x^2 + 10 x^3/((-1 + x)^3 (-1 + 2 x)^2)), {x, 0, 20}], x]

Prog

(Python)
def A362526(n): return (n+2<<n)+((n-7)*n>>1)-2 # Chai Wah Wu, Apr 24 2023

Crossrefs

Sequence in context: A152619 A051662 A326247 * A225918 A367669 A231999

Adjacent sequences: A362523 A362524 A362525 * A362527 A362528 A362529

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 24 2023

Status

approved