A358800 Number of (undirected) paths in the grid graph P_4 X P_n.

6, 146, 1618, 14248, 111030, 801756, 5493524, 36213404, 231727206, 1448346368, 8882264970, 53630707124, 319658314238, 1884696886358, 11010327107946, 63818465537674, 367417387464528, 2102996368589366, 11976130801913690, 67900925937645280, 383491738397537356

Offset: 1

Author

Seiichi Manyama, Dec 01 2022

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (27,-318,2162,-9476,28327,-59457,88270,-90466, 57194,-9664,-20392, 21783,-8809,-724,2316,-732,-135,99,0,-4).

Crossrefs

Row 4 of A288518.

Formula

G.f.: x*(6 - 16*x - 416*x^2 + 4018*x^3 - 17938*x^4 + 50228*x^5 - 97356*x^6 + 131868*x^7 - 116556*x^8 + 55784*x^9 - 2296*x^10 - 18094*x^11 + 20784*x^12 - 12882*x^13 + 1542*x^14 + 1748*x^15 - 430*x^16 - 4*x^17 - 24*x^18 - 2*x^19 + 4*x^20)/((1 - x)^2*(1 - 3*x + x^2)*(1 - 7*x + 12*x^2 - 7*x^3 + 3*x^4 + 2*x^5)^2*(1 - 8*x + 15*x^2 - 5*x^3 - 9*x^4 + 2*x^5 + x^6)). - Andrew Howroyd, Jan 27 2023

Extensions

Terms a(14) and beyond from Andrew Howroyd, Jan 27 2023