A390501 a(n) = floor((4^n - 3^n - n + 2)/2).

1, 3, 18, 86, 389, 1681, 7096, 29484, 121227, 494759, 2008574, 8122882, 32757265, 131826237, 529696452, 2125960280, 8525364503, 34166028115, 136857822730, 548012421678, 2193793078941, 8780402492393, 35137300499408, 140596273587076, 562526309116579

Offset

1,2

Comments

Also the arboricity of the n-Keller graph.

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Arboricity.

Eric Weisstein's World of Mathematics, Keller Graph.

Index entries for linear recurrences with constant coefficients, signature (8,-18,4,19,-12).

Formula

a(n) = 8*a(n-1)-18*a(n-2)+4*a(n-3)+19*a(n-4)-12*a(n-5).

G.f.: x*(1-5*x+12*x^2-8*x^3-6*x^4)/((-1+x)^2*(1-6*x+5*x^2+12*x^3)).

Mathematica

Table[Floor[(4^n - 3^n - n + 2)/2], {n, 20}]
Table[(3 - (-1)^n + 2^(2 n + 1) - 2 3^n - 2 n)/4, {n, 20}]
LinearRecurrence[{8, -18, 4, 19, -12}, {1, 3, 18, 86, 389}, 20]
CoefficientList[Series[(1 - 5 x + 12 x^2 - 8 x^3 - 6 x^4)/((-1 + x)^2 (1 - 6 x + 5 x^2 + 12 x^3)), {x, 0, 20}], x]

Prog

(Python)
def A390501(n): return (1<<(n<<1)-1)-(3**n+n-1>>1) # Chai Wah Wu, Jan 30 2026

Crossrefs

Sequence in context: A119424 A301996 A218924 * A396619 A037295 A290331

Adjacent sequences: A390498 A390499 A390500 * A390502 A390503 A390504

Keyword

nonn,easy

Author

Eric W. Weisstein, Jan 30 2026

Status

approved