A367248 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 7.

0, 5, 111, 1601, 19095, 204545, 2045511, 19508081, 179752215, 1613908385, 14202967911, 123028446161, 1052237271735, 8907026785025, 74758478722311, 623053865857841, 5162154289325655, 42558224511290465, 349394287423788711, 2858263098464575121, 23311522539676521975

Offset

1,2

Comments

a(n) is the number of n-digit numbers in A366964.

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-146,336).

Formula

a(n) = 23*8^(n-1) - 41*7^(n-1) + 3*6^n.

a(n) = 21*a(n-1) - 146*a(n-2) + 336*a(n-3) for n > 3.

O.g.f.: x^2*(5 + 6*x)/((1 - 6*x)*(1 - 7*x)*(1 - 8*x)).

E.g.f.: (161*exp(8*x) - 328*exp(7*x) + 168*exp(6*x) - 1)/56.

Mathematica

LinearRecurrence[{21, -146, 336}, {0, 5, 111}, 21]

Crossrefs

Cf. A366964.

Cf. A000400, A000420, A001018.

Cf. A367243, A367244, A367245, A367246, A367247, A367249, A367250.

Sequence in context: A322631 A294965 A219161 * A284461 A002400 A268404

Adjacent sequences: A367245 A367246 A367247 * A367249 A367250 A367251

Keyword

nonn,base,easy

Author

Stefano Spezia, Nov 11 2023

Status

approved