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A229280

Number of ascending runs in {1,...,6}^n.

0, 6, 57, 468, 3564, 25920, 182736, 1259712, 8538048, 57106944, 377913600, 2479113216, 16144468992, 104485552128, 672625741824, 4310029025280, 27505821597696, 174908814262272, 1108696193630208, 7007637010120704, 44178581150760960, 277868041444786176

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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 (12,-36).

FORMULA

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

a(n) = 6^(n-1)*(7*n+5)/2 for n>0, a(0) = 0.

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

E.g.f.: (exp(6*x)*(42*x + 5) - 5)/12.

a(n) = 12*a(n-1) - 36*a(n-2) for n > 2. (End)

MAPLE

a:= n-> `if`(n=0, 0, 6^(n-1)*(7*n+5)/2):

seq(a(n), n=0..30);

CROSSREFS

Column k=6 of A229079.

Sequence in context: A001593 A261740 A296027 * A124546 A144070 A095900

Adjacent sequences: A229277 A229278 A229279 * A229281 A229282 A229283

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Sep 18 2013

STATUS

approved

URL: https://oeis.org/A229280

⇱ A229280 - OEIS