A229278 Number of ascending runs in {1,...,4}^n.

0, 4, 26, 144, 736, 3584, 16896, 77824, 352256, 1572864, 6946816, 30408704, 132120576, 570425344, 2449473536, 10468982784, 44560285696, 188978561024, 798863917056, 3367254360064, 14156212207616, 59373627899904, 248489627877376, 1037938976620544

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-16).

Formula

G.f.: -2*(3*x-2)*x/(4*x-1)^2.

a(n) = 2^(2*n-3)*(5*n+3) for n>0, a(0) = 0.

From Elmo R. Oliveira, Nov 20 2025: (Start)

E.g.f.: (exp(4*x)*(20*x + 3) - 3)/8.

a(n) = 8*a(n-1) - 16*a(n-2) for n > 2. (End)

Maple

a:= n-> `if`(n=0, 0, 2^(2*n-3)*(5*n+3)):
seq(a(n), n=0..30);

Crossrefs

Column k=4 of A229079.

Sequence in context: A316539 A197964 A100236 * A180226 A325587 A223627

Adjacent sequences: A229275 A229276 A229277 * A229279 A229280 A229281

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 18 2013

Status

approved