A383200 Number of positive integers with n digits in which adjacent digits differ by at most 5.

9, 74, 610, 5020, 41317, 340050, 2798709, 23034169, 189577752, 1560278726, 12841536934, 105689495131, 869854553902, 7159149960981, 58921836913893, 484943447787706, 3991222267830858, 32848892512931768, 270355712339865433, 2225104276073281126, 18313239977617203949

Offset: 1

Author

Edwin Hermann, Apr 19 2025

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (8,3,-9,-1,2).

Crossrefs

Cf. A235163, A383197, A383198, A383199, A383201, A383202.

Programs

Mathematica

Rest[CoefficientList[Series[-x*(2*x^4-x^3-9*x^2+2*x+9)/((x+1)*(2*x^4-3*x^3-6*x^2+9*x-1)),{x,0,21}],x]] (* or *) LinearRecurrence[{8,3,-9,-1,2},{9,74,610,5020,41317},21] (* James C. McMahon, May 08 2025 *)

Formula

G.f.: -x*(2*x^4-x^3-9*x^2+2*x+9)/((x+1)*(2*x^4-3*x^3-6*x^2+9*x-1)). - Alois P. Heinz, Apr 26 2025

Extensions

a(11)-a(21) from Alois P. Heinz, Apr 26 2025