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A124807
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Number of base-6 circular n-digit numbers with adjacent digits differing by 2 or less.
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5
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1, 6, 24, 84, 332, 1336, 5478, 22658, 94196, 392664, 1639274, 6849002, 28627874, 119688094, 500456806, 2092720174, 8751273556, 36596513060, 153042707976, 640011807436, 2676483843602, 11192882945426, 46807955443900
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OFFSET
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0,2
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COMMENTS
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[Empirical] a(base,n) = a(base-1,n) + A005191(n+1) for base >= 2*floor(n/2) + 1.
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LINKS
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FORMULA
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G.f.: (1 - 6*x^2 - 16*x^3 + 15*x^4 + 8*x^5 - 5*x^6) / ((1 - 4*x - x^2 + x^3)*(1 - 2*x - x^2 + x^3)).
a(n) = 6*a(n-1) - 6*a(n-2) - 8*a(n-3) + 5*a(n-4) + 2*a(n-5) - a(n-6) for n > 6.
(End)
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MATHEMATICA
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LinearRecurrence[{6, -6, -8, 5, 2, -1}, {1, 6, 24, 84, 332, 1336, 5478}, 35] (* G. C. Greubel, Aug 04 2023 *)
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PROG
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(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>2)+($[(i+1)mod N]`-$[i]`>2))
(Magma) I:=[1, 6, 24, 84, 332, 1336, 5478]; [n le 7 select I[n] else 6*Self(n-1) -6*Self(n-2) -8*Self(n-3) +5*Self(n-4) +2*Self(n-5) -Self(n-6): n in [1..41]]; // G. C. Greubel, Aug 04 2023
(SageMath)
@CachedFunction
if (n<7): return (1, 6, 24, 84, 332, 1336, 5478)[n]
else: return 6*a(n-1) -6*a(n-2) -8*a(n-3) +5*a(n-4) +2*a(n-5) -a(n-6)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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