A378023 a(n) = (2*n^3 - 6*n^2 + 19*n - 9)*n/6.

1, 7, 24, 66, 155, 321, 602, 1044, 1701, 2635, 3916, 5622, 7839, 10661, 14190, 18536, 23817, 30159, 37696, 46570, 56931, 68937, 82754, 98556, 116525, 136851, 159732, 185374, 213991, 245805, 281046, 319952, 362769, 409751, 461160, 517266, 578347, 644689

Offset

1,2

Comments

For n >= 3, a(n) is also the number of minimal edge cuts in the n-Moebius ladder graph.

Links

Table of n, a(n) for n=1..38.

Eric Weisstein's World of Mathematics, Minimal Edge Cut.

Eric Weisstein's World of Mathematics, Moebius Ladder.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+1*a(n-5).

Mathematica

Table[(2 n^3 - 6 n^2 + 19 n - 9) n/6, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 7, 24, 66, 155}, 20]
CoefficientList[Series[(-1 - 2 x + x^2 - 6 x^3)/(-1 + x)^5, {x, 0, 20}], x]

Prog

(Python)
def A378023(n): return n*(n*(n*(n-3<<1)+19)-9)//6 # Chai Wah Wu, Nov 14 2024
(Magma) [(2*n^3 - 6*n^2 + 19*n - 9)*n/6 : n in [1..60]]; // Wesley Ivan Hurt, Jun 26 2025

Crossrefs

Sequence in context: A211382 A217746 A211381 * A339254 A305676 A101903

Adjacent sequences: A378020 A378021 A378022 * A378024 A378025 A378026

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 14 2024

Status

approved