A367246 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 5.

0, 9, 139, 1419, 12079, 92859, 669319, 4617699, 30878959, 201792939, 1295974999, 8212422579, 51499341439, 320287850619, 1978857202279, 12161478061059, 74421280021519, 453832688077899, 2759692966903159, 16742329188365139, 101377580843991199, 612894508749226779, 3700556151386869639

Offset

1,2

Comments

a(n) is the number of n-digit numbers in A366962.

Links

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (15,-74,120).

Formula

a(n) = 29*6^(n-1) - 49*5^(n-1) + 5*4^n.

a(n) = 15*a(n-1) - 74*a(n-2) + 120*a(n-3) for n > 3.

O.g.f.: x^2*(9 + 4*x)/((1 - 4*x)*(1 - 5*x)*(1 - 6*x)).

E.g.f.: (145*exp(6*x) - 294*exp(5*x) + 150*exp(4*x) - 1)/30.

Mathematica

LinearRecurrence[{15, -74, 120}, {0, 9, 139}, 23]

Crossrefs

Cf. A366962.

Cf. A000302, A000351, A000400.

Cf. A367243, A367244, A367245, A367247, A367248, A367249, A367250.

Sequence in context: A112702 A367426 A296394 * A322576 A350925 A243673

Adjacent sequences: A367243 A367244 A367245 * A367247 A367248 A367249

Keyword

nonn,base,easy

Author

Stefano Spezia, Nov 11 2023

Status

approved