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A308585
a(n) = 2^(n + 3) - 10*n - 6.
0
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
Eric Weisstein's World of Mathematics, Graph Path
Eric Weisstein's World of Mathematics, Triangular Snake Graph
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)).
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 08 2019
STATUS
approved