A367247 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 6.

0, 7, 131, 1609, 16415, 150817, 1296191, 10641169, 84520175, 654958177, 4980233951, 37312922929, 276288797135, 2026564724737, 14750977566911, 106695818055889, 767748717541295, 5500729672814497, 39270143125479071, 279511731951144049, 1984459091985376655, 14059238393314971457

Offset

1,2

Comments

a(n) is the number of n-digit numbers in A366963.

Links

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (18,-107,210).

Formula

a(n) = 27*7^(n-1) - 47*6^(n-1) + 4*5^n.

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

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

E.g.f.: (162*exp(7*x) - 329*exp(6*x) + 168*exp(5*x) - 1)/42.

Mathematica

LinearRecurrence[{18, -107, 210}, {0, 7, 131}, 22]

Crossrefs

Cf. A366963.

Cf. A000351, A000400, A000420.

Cf. A367243, A367244, A367245, A367246, A367248, A367249, A367250.

Sequence in context: A074224 A158701 A201308 * A170912 A099601 A028420

Adjacent sequences: A367244 A367245 A367246 * A367248 A367249 A367250

Keyword

nonn,base,easy

Author

Stefano Spezia, Nov 11 2023

Status

approved