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A126393
Number of base 6 n-digit numbers with adjacent digits differing by two or less.
4
1, 6, 24, 100, 418, 1748, 7310, 30570, 127842, 534628, 2235784, 9349922, 39100844, 163517514, 683820978, 2859700582, 11959105792, 50012302772, 209148616298, 874647662172, 3657726962214, 15296406894730, 63968706878962
OFFSET
0,2
COMMENTS
a(base,n) = a(base-1,n) + 5^(n-1) for base >= 2*n - 1.
a(base,n) = a(base-1,n) + 5^(n-1) - 2 when base = 2*(n-1).
LINKS
Sergey Kitaev and Jeffrey Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.
FORMULA
G.f.: 1 + 2*x*(3-x^2)/(1-4*x-x^2+x^3). - R. J. Mathar, Jun 06 2013
a(n) = [n=0] + 6*A364705(n) - 2*A364705(n-2). - G. C. Greubel, Aug 08 2023
MATHEMATICA
LinearRecurrence[{4, 1, -1}, {1, 6, 24, 100}, 41] (* G. C. Greubel, Aug 08 2023 *)
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>2)+($[i+1]`-$[i]`>2))
(Magma) I:=[1, 6, 24, 100]; [n le 4 select I[n] else 4*Self(n-1) +Self(n-2) -Self(n-3): n in [1..41]]; // G. C. Greubel, Aug 08 2023
(SageMath)
@CachedFunction
def a(n): # A126393
if (n<4): return (1, 6, 24, 100)[n]
else: return 4*a(n-1) +a(n-2) -a(n-3)
[a(n) for n in range(41)] # G. C. Greubel, Aug 08 2023
CROSSREFS
Cf. Base 6 differing by one or less A126360.
Cf. A364705.
Sequence in context: A343116 A360036 A255471 * A265697 A120583 A089378
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 28 2006
STATUS
approved