A384711 Expansion of (1+x) / (1-2*x-6*x^2).
1, 3, 12, 42, 156, 564, 2064, 7512, 27408, 99888, 364224, 1327776, 4840896, 17648448, 64342272, 234575232, 855204096, 3117859584, 11366943744, 41441044992, 151083752448, 550813774848, 2008130064384, 7321142777856, 26691065942016, 97308988551168
Offset: 0
Examples
a(2)=12 because we have the walks 0-1-0, 0-1-2, 0-1-3, 0-1-4, 0-3-0, 0-3-1, 0-3-2, 0-3-4, 0-4-0, 0-4-1, 0-4-2, 0-4-3.
Links
- Sean A. Irvine, Walks on Graphs.
Programs
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Maple
a:= n-> (<<0|1|0|1|1>, <1|0|1|1|1>, <0|1|0|1|1>, <1|1|1|0|1>, <1|1|1|1|0>>^n. <<1, 1, 1, 1, 1>>)[1, 1]: seq(a(n), n=0..32);
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Mathematica
CoefficientList[Series[(1+x) / (1-2*x-6*x^2), {x, 0, 32}], x]
Formula
a(n) = 3*A133592(n)/2 for n>0.
Comments