A359620 -id:A359620 - cp's OEIS frontend

A359621 Number of edge cuts in the n-prism graph.

1, 4, 31, 314, 3013, 27060, 232671, 1947118, 16021801, 130447976, 1055068595, 8498016994, 68269451069, 547562782044, 4387403278023, 35132904838614, 281226897433681, 2250607478637648, 18008682685966299, 144087851840540874, 1152791046751807845

Offset: 0

Eric W. Weisstein, Jan 07 2023

nonn

The n-prism graph is defined from n >= 3. The sequence has been extrapolated to n = 0 using the recurrence. - Andrew Howroyd, Jan 26 2023

Andrew Howroyd, Table of n, a(n) for n = 0..200
Eric Weisstein's World of Mathematics, Edge Cut
Eric Weisstein's World of Mathematics, Prism Graph
Index entries for linear recurrences with constant coefficients, signature (20, -146, 488, -777, 612, -228, 32).

Cf. A359620.

Table[2 + 8^n + n + (((17^(-1/2) - 1) n - 2) (5 + Sqrt[17])^n - ((17^(-1/2) + 1) n + 2) (5 - Sqrt[17])^n)/2^(n + 1), {n, 0, 20}] // Expand (* Eric W. Weisstein, Dec 01 2024 *)
LinearRecurrence[{20, -146, 488, -777, 612, -228, 32}, {1, 4, 31, 314, 3013, 27060, 232671}, 20] (* Eric W. Weisstein, Dec 01 2024 *)
CoefficientList[Series[-(1 - 16 x + 97 x^2 - 210 x^3 + 84 x^4 + 12 x^5 + 4 x^6)/((-1 + x)^2 (-1 + 8 x) (1 - 5 x + 2 x^2)^2), {x, 0, 20}], x]

Vec((1 - 16*x + 97*x^2 - 210*x^3 + 84*x^4 + 12*x^5 + 4*x^6)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2) + O(x^21)) \\ Andrew Howroyd, Jan 26 2023

G.f.: (1 - 16*x + 97*x^2 - 210*x^3 + 84*x^4 + 12*x^5 + 4*x^6)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2). - Andrew Howroyd, Jan 26 2023

a(n) = 20*a(n-1)-146*a(n-2)+488*a(n-3)-777*a(n-4)+612*a(n-5)-228*a(n-6)+32*a(n-7). - Eric W. Weisstein, Dec 01 2024

a(0)-a(2) prepended and terms a(8) and beyond from Andrew Howroyd, Jan 26 2023

A378922 Number of minimal edge cuts in the n-antiprism graph.

Original entry on oeis.org

1, 1, 7, 28, 81, 191, 391, 722, 1233, 1981, 3031, 4456, 6337, 8763, 11831, 15646, 20321, 25977, 32743, 40756, 50161, 61111, 73767, 88298, 104881, 123701, 144951, 168832, 195553, 225331, 258391, 294966, 335297, 379633, 428231, 481356, 539281, 602287, 670663, 744706, 824721

Offset: 0

Eric W. Weisstein, Dec 11 2024

The n-antiprism graph is defined for n >= 3. The sequence has been extended to n = 0 using the formula. - Andrew Howroyd, Jun 09 2025

Andrew Howroyd, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Antiprism Graph.
Eric Weisstein's World of Mathematics, Minimal Edge Cut.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A359620.

a(n) = (2*n^4 - 3*n^3 + 13*n^2 - 12*n + 6)/6 \\ Andrew Howroyd, Jun 09 2025

From Andrew Howroyd, Jun 09 2025: (Start)
a(n) = 1 + 2*n*(n-1) + n^2*(n-1)*(2*n-1)/6.
a(n) = (2*n^4 - 3*n^3 + 13*n^2 - 12*n + 6)/6. (End)
From Elmo R. Oliveira, Sep 03 2025: (Start)
G.f.: (1 - 4*x + 12*x^2 - 7*x^3 + 6*x^4)/(1-x)^5.
E.g.f.: (6 + 18*x^2 + 9*x^3 + 2*x^4)*exp(x)/6.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)

a(0)-a(2) prepended and a(7) onwards from Andrew Howroyd, Jun 09 2025

cp's OEIS Frontend

A359621 Number of edge cuts in the n-prism graph.

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