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A126364 Number of base 10 n-digit numbers with adjacent digits differing by one or less. 6
10, 28, 80, 230, 664, 1922, 5574, 16188, 47064, 136946, 398746, 1161634, 3385486, 9869934, 28781908, 83948652, 244894048, 714493794, 2084792450, 6083620812, 17753709802, 51812911858, 151218254846, 441351052720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

[Empirical] a(base,n)=a(base-1,n)+3^(n-1) for base>=n; a(base,n)=a(base-1,n)+3^(n-1)-2 when base=n-1.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-10,1,6,-1).

FORMULA

G.f.: (1 + 4*x - 22*x^2 + 11*x^3 + 14*x^4 - 3*x^5)/(1 - 6*x + 10*x^2 - x^3 - 6*x^4 + x^5). - Alexander R. Povolotsky_, Aug 18 2011

Conjecture: a(n) = 3*a(n-1) - A025565(n), n >= 2. - Daniel Forgues, Aug 23 2011

MATHEMATICA

CoefficientList[ Series[(1 + 4x - 22x^2 + 11x^3 + 14x^4 - 3x^5)/(1 - 6x + 10x^2 - x^3 - 6x^4 + x^5), {x, 0, 24}], x] (* Robert G. Wilson v, Aug 19 2011 *)

LinearRecurrence[{6, -10, 1, 6, -1}, {10, 28, 80, 230, 664}, 30] (* Vincenzo Librandi, Mar 21 2015 *)

PROG

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>1)+($[i+1]`-$[i]`>1))

(PARI) Vec((1+4*x-22*x^2+11*x^3+14*x^4-3*x^5)/(1-6*x+10*x^2-x^3-6*x^4+x^5)+O(x^99)) \\ Charles R Greathouse IV, Aug 23 2011

CROSSREFS

Sequence in context: A048491 A124703 A251319 * A076712 A116973 A264579

Adjacent sequences:  A126361 A126362 A126363 * A126365 A126366 A126367

KEYWORD

nonn,base,easy

AUTHOR

R. H. Hardin, Dec 26 2006

STATUS

approved

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Last modified March 29 03:14 EDT 2017. Contains 284250 sequences.