A229279 Number of ascending runs in {1,...,5}^n.

0, 5, 40, 275, 1750, 10625, 62500, 359375, 2031250, 11328125, 62500000, 341796875, 1855468750, 10009765625, 53710937500, 286865234375, 1525878906250, 8087158203125, 42724609375000, 225067138671875, 1182556152343750, 6198883056640625, 32424926757812500

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 (10,-25).

Formula

G.f.: -5*(2*x-1)*x/(5*x-1)^2.

a(n) = 5^(n-1)*(3*n+2) for n>0, a(0) = 0.

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

E.g.f.: (exp(5*x)*(15*x + 2) - 2)/5.

a(n) = 10*a(n-1) - 25*a(n-2) for n > 2. (End)

Maple

a:= n-> `if`(n=0, 0, 5^(n-1)*(3*n+2)):
seq(a(n), n=0..30);

Crossrefs

Column k=5 of A229079.

Sequence in context: A157794 A001656 A087632 * A124306 A124545 A125729

Adjacent sequences: A229276 A229277 A229278 * A229280 A229281 A229282

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 18 2013

Status

approved