A124864 Number of base 13 circular n-digit numbers with adjacent digits differing by 2 or less.

1, 13, 59, 217, 927, 4003, 17735, 79603, 361207, 1652347, 7608009, 35214643, 163703859, 763777807, 3574392251, 16771283857, 78867271271, 371585266531, 1753627967177, 8287756490659, 39216985201477, 185770958749075

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+A005191(n+1) for base>=2.int(n/2)+1.

See A285280 for confirmation of linear recurrence and code to produce sequence. - Ray Chandler, Aug 12 2023.

Links

Ray Chandler, Table of n, a(n) for n = 0..99

OEIS Wiki, Number of base k circular n-digit numbers with adjacent digits differing by d or less

Index entries for linear recurrences with constant coefficients, signature (13, -55, 55, 159, -285, -155, 365, 60, -174, -9, 27).

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>2)+($[(i+1)mod N]`-$[i]`>2))
(PARI) Vec((1-55*x^2+110*x^3+477*x^4-1140*x^5-775*x^6+2190*x^7+420*x^8-1392*x^9-81*x^10+270*x^11)/(1-13*x+55*x^2-55*x^3-159*x^4+285*x^5+155*x^6-365*x^7-60*x^8+174*x^9+9*x^10-27*x^11)+O(x^99)) \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. Row 13 of A285280.

Cf. A005191.

Sequence in context: A141917 A163833 A213567 * A126400 A297962 A354670

Adjacent sequences: A124861 A124862 A124863 * A124865 A124866 A124867

Keyword

nonn,base,easy

Author

R. H. Hardin, Dec 28 2006

Status

approved