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

1,1

Links

Table of n, a(n) for n=1..21.

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

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

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 *)

Crossrefs

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

Sequence in context: A037533 A178827 A190984 * A001716 A372843 A231910

Adjacent sequences: A383197 A383198 A383199 * A383201 A383202 A383203

Keyword

nonn,base,easy

Author

Edwin Hermann, Apr 19 2025

Extensions

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

Status

approved