A383198 Number of positive integers with n digits in which adjacent digits differ by at most 3.

9, 54, 328, 2000, 12202, 74458, 454366, 2772710, 16920138, 103253214, 630091042, 3845059318, 23464039746, 143186649814, 873780342786, 5332145758694, 32538816680050, 198564450196598, 1211717109125762, 7394366670845606, 45123286657530514, 275359755529253142

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,-4,-10,6).

Formula

G.f.: -x*(10*x^3-14*x^2-9*x+9)/(6*x^4-10*x^3-4*x^2+7*x-1). - Alois P. Heinz, Apr 23 2025

Mathematica

LinearRecurrence[{7, -4, -10, 6}, {9, 54, 328, 2000}, 22] (* James C. McMahon, May 01 2025 *)
(* Alternative: *)
Rest[CoefficientList[Series[(-x*(10*x^3-14*x^2-9*x+9)/(6*x^4-10*x^3-4*x^2+7*x-1)), {x, 0, 22}], x]] (* James C. McMahon, May 01 2025 *)

Crossrefs

Cf. A235163, A383197, A383199, A383200, A383201, A383202.

Sequence in context: A115784 A037599 A037704 * A093847 A363415 A157539

Adjacent sequences: A383195 A383196 A383197 * A383199 A383200 A383201

Keyword

nonn,base,easy

Author

Edwin Hermann, Apr 19 2025

Extensions

More terms from Alois P. Heinz, Apr 23 2025

Status

approved