A378023 - OEIS

%I #12 Jun 26 2025 10:31:34

%S 1,7,24,66,155,321,602,1044,1701,2635,3916,5622,7839,10661,14190,

%T 18536,23817,30159,37696,46570,56931,68937,82754,98556,116525,136851,

%U 159732,185374,213991,245805,281046,319952,362769,409751,461160,517266,578347,644689

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

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalEdgeCut.html">Minimal Edge Cut</a>.

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

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

%t Table[(2 n^3 - 6 n^2 + 19 n - 9) n/6, {n, 20}]

%t LinearRecurrence[{5, -10, 10, -5, 1}, {1, 7, 24, 66, 155}, 20]

%t CoefficientList[Series[(-1 - 2 x + x^2 - 6 x^3)/(-1 + x)^5, {x, 0, 20}], x]

%o (Python)

%o def A378023(n): return n*(n*(n*(n-3<<1)+19)-9)//6 # _Chai Wah Wu_, Nov 14 2024

%o (Magma) [(2*n^3 - 6*n^2 + 19*n - 9)*n/6 : n in [1..60]]; // _Wesley Ivan Hurt_, Jun 26 2025

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Nov 14 2024