A125373 Number of base 10 circular n-digit numbers with adjacent digits differing by 5 or less.

1, 10, 80, 580, 4660, 37960, 311378, 2559658, 21057948, 173287588, 1426133270, 11737272106, 96600478510, 795047628502, 6543462720560, 53854541701240, 443238127915788, 3647975524214452, 30023874009147704, 247105006940966092

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+F(5) for base>=5.int(n/2)+1 and F(d) is the largest coefficient in (1+x+...+x^(2d))^n

Links

Table of n, a(n) for n=0..19.

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 (11, -21, -19, 34, 8, -15, -1, 2).

Formula

G.f.: (1 - x - 9*x^2 - 71*x^3 + 116*x^4 + 52*x^5 - 87*x^6 - 9*x^7 + 16*x^8)/((1 + x)(1 - 3*x + x^3)(1 - 9*x + 6*x^2 + 3*x^3 - 2*x^4)). For n<4, a(n) = 5*6^n-4*5^n = A257286(n). - M. F. Hasler, May 03 2015

Mathematica

LinearRecurrence[{11, -21, -19, 34, 8, -15, -1, 2}, {1, 10, 80, 580, 4660, 37960, 311378, 2559658, 21057948}, 30] (* Harvey P. Dale, May 14 2018 *)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>5)+($[(i+1)mod N]`-$[i]`>5))

Crossrefs

Cf. A257286.

Sequence in context: A374511 A377199 A257286 * A093145 A341917 A369474

Adjacent sequences: A125370 A125371 A125372 * A125374 A125375 A125376

Keyword

nonn,base,easy

Author

R. H. Hardin, Dec 28 2006

Status

approved