A125372 Number of base-9 circular n-digit numbers with adjacent digits differing by 5 or less.

1, 9, 69, 489, 3773, 29359, 229371, 1793675, 14030597, 109759917, 858660839, 6717419531, 52551380915, 411117567181, 3216236722495, 25161121675789, 196839383096437, 1539905230937741, 12046919094905577, 94244929368967819

Offset

0,2

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-6,-26,5,17,-1,-3).

Formula

G.f.: (1 - 6*x^2 - 52*x^3 + 15*x^4 + 68*x^5 - 5*x^6 - 18*x^7)/((1 + x)*(1 - 2*x - x^2 + x^3)*(1 - 8*x + x^2 + 3*x^3)). - M. F. Hasler, May 03 2015

For n < 4, a(n) = 4*6^n - 3*5^n. - M. F. Hasler, May 03 2015

a(n) = 9*a(n-1) - 6*a(n-2) - 26*a(n-3) + 5*a(n-4) + 17*a(n-5) - a(n-6) - 3*a(n-7) for n > 7. - Wesley Ivan Hurt, Oct 08 2017

Mathematica

CoefficientList[Series[(1 - 6*x^2 - 52*x^3 + 15*x^4 + 68*x^5 - 5*x^6 - 18*x^7)/((1 + x)*(1 - 2*x - x^2 + x^3)*(1 - 8*x + x^2 + 3*x^3)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 08 2017 *)

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

Sequence in context: A196490 A297593 A198691 * A165147 A075045 A361139

Adjacent sequences: A125369 A125370 A125371 * A125373 A125374 A125375

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved