A367244 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 3.

0, 13, 119, 733, 3815, 18133, 81599, 354493, 1504055, 6278053, 25904879, 106011853, 431253095, 1746686773, 7051884959, 28403182813, 114200118935, 458563556293, 1839545301839, 7374058107373, 29543870469575, 118318410678613, 473702458475519, 1896096339905533, 7588244995073015

Offset

1,2

Comments

a(n) is the number of n-digit numbers in A366960.

Links

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (9,-26,24).

Formula

a(n) = 27*4^(n-1) - 41*3^(n-1) + 7*2^n.

a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3) for n > 3.

O.g.f.: x^2*(13 + 2*x)/((1 - 2*x)*(1 - 3*x)*(1 - 4*x)).

E.g.f.: (exp(x) - 1)^2*(81*exp(2*x) - 2*exp(x) - 1)/12.

Mathematica

LinearRecurrence[{9, -26, 24}, {0, 13, 119}, 25]

Crossrefs

Cf. A366960.

Cf. A000079, A000244, A000302.

Cf. A367243, A367245, A367246, A367247, A367248, A367249, A367250.

Sequence in context: A016295 A225965 A051824 * A016285 A121086 A159969

Adjacent sequences: A367241 A367242 A367243 * A367245 A367246 A367247

Keyword

nonn,base,easy

Author

Stefano Spezia, Nov 11 2023

Status

approved