A126544 Number of base 23 n-digit numbers with adjacent digits differing by five or less.

1, 23, 223, 2233, 22593, 229845, 2344951, 23959555, 244996403, 2506196601, 25642541441, 262394013219, 2685165779179, 27478998106253, 281214182348803, 2877908167110333, 29452244633456589, 301412164854186481

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5

Links

Table of n, a(n) for n=0..17.

Formula

G.f.: -(2*x^11 -7*x^10 -24*x^9 +89*x^8 +67*x^7 -302*x^6 -20*x^5 +327*x^4 -56*x^3 -80*x^2 +8*x +1) / (x^11 -5*x^10 -9*x^9 +62*x^8 +3*x^7 -202*x^6 +65*x^5 +207*x^4 -90*x^3 -42*x^2 +15*x -1). - Alois P. Heinz, Sep 25 2015

Mathematica

CoefficientList[Series[-(2x^11-7x^10-24x^9+89x^8+67x^7-302x^6-20x^5+327x^4-56x^3-80x^2+8x+1)/(x^11-5x^10-9x^9+62x^8+3x^7- 202x^6+ 65x^5+ 207x^4- 90x^3- 42x^2+15x-1), {x, 0, 50}], x] (* Harvey P. Dale, Sep 25 2024 *)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>5)+($[i+1]`-$[i]`>5))

Crossrefs

Cf. Base 23 differing by four or less A126518, three or less A126491, two or less A126410, one or less A126377.

Sequence in context: A244766 A125386 A091628 * A272796 A285552 A206766

Adjacent sequences: A126541 A126542 A126543 * A126545 A126546 A126547

Keyword

nonn,base,changed

Author

R. H. Hardin, Dec 28 2006

Status

approved