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A307921
Number of (undirected) paths in the n-book graph.
0
12, 49, 136, 297, 556, 937, 1464, 2161, 3052, 4161, 5512, 7129, 9036, 11257, 13816, 16737, 20044, 23761, 27912, 32521, 37612, 43209, 49336, 56017, 63276, 71137, 79624, 88761, 98572, 109081, 120312, 132289, 145036, 158577, 172936, 188137, 204204, 221161, 239032
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Graph Path
FORMULA
a(n) = 4*n^3 + n^2 + 6*n + 1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: x*(12 + x + 12*x^2 - x^3)/(-1 + x)^4.
MATHEMATICA
Table[4 n^3 + n^2 + 6 n + 1, {n, 20}]
LinearRecurrence[{4, -6, 4, -1}, {12, 49, 136, 297}, 20]
CoefficientList[Series[(12 + x + 12 x^2 - x^3)/(-1 + x)^4, {x, 0, 20}], x]
CROSSREFS
Sequence in context: A009950 A252178 A218832 * A288516 A219153 A318404
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, May 06 2019
STATUS
approved