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a(n) = 2^(n + 3) - 10*n - 6.
0

%I #5 Jun 09 2019 01:25:02

%S 0,6,28,82,200,446,948,1962,4000,8086,16268,32642,65400,130926,261988,

%T 524122,1048400,2096966,4194108,8388402,16777000,33554206,67108628,

%U 134217482,268435200,536870646,1073741548,2147483362,4294967000,8589934286,17179868868,34359738042

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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphPath.html">Graph Path</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularSnakeGraph.html">Triangular Snake Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 2).

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

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

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

%t Table[2^(3 + n) - 10 n - 6, {n, 20}]

%t LinearRecurrence[{4, -5, 2}, {0, 6, 28}, 20]

%t CoefficientList[Series[-2 x (3 + 2 x)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x]

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Jun 08 2019