A379741 Number of cyclic edge cuts in the (2n-1)-triangular snake graph.

0, 0, 0, 3, 81, 1374, 18738, 224649, 2473443, 25639428, 254139876, 2433890895, 22685594805, 206878779882, 1853184109014, 16356052422741, 142570655572167, 1229696463806736, 10511110759078152, 89151460774796187, 751086607464533529, 6290887041127983990

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

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

Eric Weisstein's World of Mathematics, Triangular Snake Graph.

Index entries for linear recurrences with constant coefficients, signature (27,-271,1197,-1960).

Formula

G.f.: 3*x^4/((1 - 5*x)*(1 - 7*x)^2*(1 - 8*x)). - Andrew Howroyd, Jan 01 2025

a(n) = (8^n - 6*(2*n+5)*7^(n-2) - 2*5^(n-1))/8. - Vincenzo Librandi, Jan 08 2025, after Andrew Howroyd

Mathematica

Table[(8^n - 6 (2 n + 5) 7^(n - 2) - 2 5^(n - 1))/8, {n, 40}] (* Vincenzo Librandi, Jan 08 2025 *)
LinearRecurrence[{27, -271, 1197, -1960}, {0, 0, 0, 3}, 39] (* Vincenzo Librandi, Jan 08 2025 *)
CoefficientList[Series[3 x^3/((-1 + 5 x) (-1 + 7 x)^2 (-1 + 8 x)), {x, 0, 20}], x] (* Eric W. Weisstein, Feb 11 2025 *)

Prog

(PARI) my(N=25); 3*Vec(1/((1 - 5*x)*(1 - 7*x)^2*(1 - 8*x)) + O(x^(N-3)), -N) \\ Andrew Howroyd, Jan 01 2025
(Magma)[(8^n - 6*(2*n+5)*7^(n-2) - 2*5^(n-1))/8: n in [1..25]]; // Vincenzo Librandi, Jan 08 2025

Crossrefs

Sequence in context: A223187 A060851 A116179 * A378311 A013732 A292974

Adjacent sequences: A379738 A379739 A379740 * A379742 A379743 A379744

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 31 2024

Extensions

a(9) onwards from Andrew Howroyd, Jan 01 2025

Status

approved