A367249 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 8.

0, 3, 79, 1323, 18175, 223323, 2555119, 27828363, 292407775, 2990349243, 29943991759, 294872615403, 2864776362175, 27525734996763, 262061152909999, 2475899571994443, 23240879960425375, 216963121865909883, 2015960236625789839, 18656492902684557483, 172056837889322101375

Offset

1,2

Comments

a(n) is the number of n-digit numbers in A366965.

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (24,-191,504).

Formula

a(n) = 17*9^(n-1) - 31*8^(n-1) + 2*7^n.

a(n) = 24*a(n-1) - 191*a(n-2) + 504*a(n-3) for n > 3.

O.g.f.: x^2*(3 + 7*x)/((1 - 7*x)*(1 - 8*x)*(1 - 9*x)).

E.g.f.: (136*exp(9*x) - 279*exp(8*x) + 144*exp(7*x) - 1)/72.

Mathematica

LinearRecurrence[{24, -191, 504}, {0, 3, 79}, 21]

Crossrefs

Cf. A366965.

Cf. A000420, A001018, A001019.

Cf. A367243, A367244, A367245, A367246, A367247, A367248, A367250.

Sequence in context: A347165 A073176 A236574 * A062660 A331673 A065399

Adjacent sequences: A367246 A367247 A367248 * A367250 A367251 A367252

Keyword

nonn,base,easy

Author

Stefano Spezia, Nov 11 2023

Status

approved