A307921 Number of (undirected) paths in the n-book graph.

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

Table of n, a(n) for n=1..39.

Eric Weisstein's World of Mathematics, Book Graph

Eric Weisstein's World of Mathematics, Graph Path

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

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

Adjacent sequences: A307918 A307919 A307920 * A307922 A307923 A307924

Keyword

nonn,easy

Author

Eric W. Weisstein, May 06 2019

Status

approved