A372093 Number of Eulerian orientations of the torus grid graph C_5 X C_n.

64, 308, 2116, 16892, 143224, 1250228, 11091536, 99371772, 895878604, 8109607248, 73605150496, 669235388612, 6091889767144, 55495316073288, 505799972171296, 4611529143198652, 42053844507644124, 383555932615158068, 3498586905231628036, 31914171636394303392

Offset

1,1

Links

Brendan McKay, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Torus Grid Graph.

Index entries for linear recurrences with constant coefficients, signature (24,-219,988,-2407,3181,-2042,292,280,-96).

Formula

a(n) = 24*a(n-1) - 219*a(n-2) + 988*a(n-3) - 2407*a(n-4) + 3181*a(n-5) - 2042*a(n-6) + 292*a(n-7) + 280*a(n-8) - 96*a(n-9).

Asymptotically, a(n) ~ 2*(5+sqrt(17))^n.

G.f.: 4*x*(16 - 307*x + 2185*x^2 - 7418*x^3 + 12741*x^4 - 10159*x^5 + 1744*x^6 + 1956*x^7 - 768*x^8) / ((-1 + x) * (-1 + 2*x) * (-1 + 6*x) * (1 - 10*x + 8*x^2) * (-1 + 5*x - 6*x^2 + x^4)). - Elmo R. Oliveira, May 12 2026

Crossrefs

Row 5 of A298119.

Cf. A298201.

Sequence in context: A299387 A299186 A299947 * A251196 A221486 A231942

Adjacent sequences: A372090 A372091 A372092 * A372094 A372095 A372096

Keyword

nonn,easy

Author

Brendan McKay, Apr 18 2024

Status

approved