A367245 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 4.

0, 11, 135, 1103, 7551, 46871, 273735, 1534943, 8366031, 44674151, 234982935, 1222071983, 6301114911, 32274971831, 164471580135, 834802180223, 4223960206191, 21320114811911, 107403378865335, 540232762595663, 2714041233191871, 13621757688226391, 68315120054438535

Offset

1,2

Comments

a(n) is the number of n-digit numbers in A366961.

Links

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (12,-47,60).

Formula

a(n) = 29*5^(n-1) - 47*4^(n-1) + 2*3^(n+1).

a(n) = 12*a(n-1) - 47*a(n-2) + 60*a(n-3) for n > 3.

O.g.f.: x^2*(11 + 3*x)/((1 - 3*x)*(1 - 4*x)*(1 - 5*x)).

E.g.f.: (116*exp(5*x) - 235*exp(4*x) + 120*exp(3*x) - 1)/20.

Mathematica

LinearRecurrence[{12, -47, 60}, {0, 11, 135}, 23]

Crossrefs

Cf. A366961.

Cf. A000244, A000302, A000351.

Cf. A367243, A367244, A367246, A367247, A367248, A367249, A367250.

Sequence in context: A014994 A015609 A250460 * A157773 A336180 A209487

Adjacent sequences: A367242 A367243 A367244 * A367246 A367247 A367248

Keyword

nonn,base,easy

Author

Stefano Spezia, Nov 11 2023

Status

approved