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

Author

Stefano Spezia, Nov 11 2023

Keywords

• nonn
• base
• easy

Comments

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

Links

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

Crossrefs

Cf. A366965.

Cf. A000420, A001018, A001019.

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

Programs

Mathematica

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

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.