A383199 Number of positive integers with n digits in which adjacent digits differ by at most 4.

9, 65, 475, 3465, 25282, 184463, 1345887, 9819916, 71648478, 522764591, 3814216651, 27829445433, 203050351876, 1481504383412, 10809413614854, 78868091114176, 575440631436879, 4198553757680021, 30633661742154286, 223510591001999469, 1630787227154056312

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,3,-6,-1,1).

Formula

G.f.: -x*(x^4-x^3-7*x^2+2*x+9)/(x^5-x^4-6*x^3+3*x^2+7*x-1). - Alois P. Heinz, Apr 23 2025

Mathematica

Rest[CoefficientList[Series[-x*(x^4-x^3-7*x^2+2*x+9)/(x^5-x^4-6*x^3+3*x^2+7*x-1), {x, 0, 21}], x]] (* or *) LinearRecurrence[{7, 3, -6, -1, 1}, {9, 65, 475, 3465, 25282}, 21] (* James C. McMahon, May 01 2025 *)

Crossrefs

Cf. A235163, A383197, A383198, A383200, A383201, A383202.

Sequence in context: A238275 A381024 A287816 * A036731 A020234 A154996

Adjacent sequences: A383196 A383197 A383198 * A383200 A383201 A383202

Keyword

nonn,base,easy

Author

Edwin Hermann, Apr 19 2025

Extensions

More terms from Alois P. Heinz, Apr 23 2025

Status

approved