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A287992
Number of (undirected) paths in the prism graph Y_n.
3
1, 26, 129, 444, 1285, 3366, 8281, 19544, 44829, 100770, 223201, 488916, 1061749, 2289854, 4910505, 10480176, 22275661, 47178234, 99605809, 209704940, 440390181, 922733526, 1929364729, 4026514824, 8388588925, 17448283346, 36238762881, 75161901444, 155692535509, 322122515310
OFFSET
1,2
COMMENTS
Extended to a(1)-a(2) using the formula.
LINKS
Eric Weisstein's World of Mathematics, Graph Path.
Eric Weisstein's World of Mathematics, Prism Graph.
FORMULA
a(n) = (5*2^(n + 1) - 5*n - n^2 - 13)*n.
From Colin Barker, Jun 04 2017: (Start)
G.f.: x*(1 + 18*x - 53*x^2 + 44*x^3 - 16*x^4) / ((1 - x)^4*(1 - 2*x)^2).
a(n) = 8*a(n-1) - 26*a(n-2) + 44*a(n-3) - 41*a(n-4) + 20*a(n-5) - 4*a(n-6) for n>6. (End)
MATHEMATICA
Table[(5 2^(n + 1) - 5 n - n^2 - 13) n, {n, 20}]
LinearRecurrence[{8, -26, 44, -41, 20, -4}, {1, 26, 129, 444, 1285, 3366}, 20]
CoefficientList[Series[(1 + 18 x - 53 x^2 + 44 x^3 - 16 x^4)/((1 - x)^4 (1 - 2 x)^2), {x, 0, 20}], x]
PROG
(PARI) Vec(x*(1 + 18*x - 53*x^2 + 44*x^3 - 16*x^4) / ((1 - x)^4*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Jun 04 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 04 2017
STATUS
approved