A367243 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 2.

0, 15, 91, 381, 1375, 4605, 14791, 46341, 142975, 436845, 1326391, 4010901, 12096175, 36415485, 109500391, 329009061, 988042975, 2966160525, 8902544791, 26715760821, 80163535375, 240523111965, 721634347591, 2165033066181, 6495359245375, 19486597829805, 58460833676791

Offset

1,2

Comments

a(n) is the number of n-digit numbers in A366959.

Links

Table of n, a(n) for n=1..27.

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

a(n) = (46*3^n - 93*2^n + 48)/6.

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 3.

O.g.f.: x^2*(15 + x)/((1 - x)*(1- 2*x)*(1 - 3*x)).

E.g.f.: (exp(x) - 1)^2*(46*exp(x) - 1)/6.

Mathematica

LinearRecurrence[{6, -11, 6}, {0, 15, 91}, 27]

Crossrefs

Cf. A366959.

Cf. A000079, A000244.

Cf. A367244, A367245, A367246, A367247, A367248, A367249, A367250.

Sequence in context: A237516 A020242 A020255 * A180248 A329759 A041428

Adjacent sequences: A367240 A367241 A367242 * A367244 A367245 A367246

Keyword

nonn,base,easy

Author

Stefano Spezia, Nov 11 2023

Status

approved