A229283 Number of ascending runs in {1,...,9}^n.

0, 9, 126, 1539, 17496, 190269, 2007666, 20726199, 210450636, 2109289329, 20920706406, 205720279659, 2008387814976, 19487638017189, 188098071296346, 1807266603941919, 17294855095950516, 164918796807813849, 1567655079768657486, 14859368894402912979

Offset: 0

Author

Alois P. Heinz, Sep 18 2013

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (18,-81).

Crossrefs

Column k=9 of A229079.

Programs

Maple

a:= n-> `if`(n=0, 0, 9^(n-1)*(5*n+4)):
seq(a(n), n=0..30);

Formula

G.f.: -9*(4*x-1)*x/(9*x-1)^2.

a(n) = 9^(n-1)*(5*n+4) for n>0, a(0) = 0.

a(n) = 18*a(n-1) - 81*a(n-2). - Wesley Ivan Hurt, May 24 2024