A308585 a(n) = 2^(n + 3) - 10*n - 6.

0, 6, 28, 82, 200, 446, 948, 1962, 4000, 8086, 16268, 32642, 65400, 130926, 261988, 524122, 1048400, 2096966, 4194108, 8388402, 16777000, 33554206, 67108628, 134217482, 268435200, 536870646, 1073741548, 2147483362, 4294967000, 8589934286, 17179868868, 34359738042

Offset

1,2

Comments

Number of (undirected) paths in the (2n-1)-triangular snake graph.

Links

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Graph Path.

Eric Weisstein's World of Mathematics, Triangular Snake Graph.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = 2^(n + 3) - 10*n - 6.

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

G.f.: -2*x^2*(3 + 2*x)/((-1 + x)^2*(-1 + 2*x)).

E.g.f.: 2*(4*exp(2*x) - (3 + 5*x)*exp(x) - 1). - Elmo R. Oliveira, Nov 14 2025

Mathematica

Table[2^(3 + n) - 10 n - 6, {n, 20}]
LinearRecurrence[{4, -5, 2}, {0, 6, 28}, 20]
CoefficientList[Series[-2 x (3 + 2 x)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A343512 A326484 A144945 * A202956 A279915 A300906

Adjacent sequences: A308582 A308583 A308584 * A308586 A308587 A308588

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 08 2019

Status

approved