A120926
Number of isolated 0's in all ternary words of length n on {0,1,2}.
Original entry on oeis.org
1, 4, 16, 60, 216, 756, 2592, 8748, 29160, 96228, 314928, 1023516, 3306744, 10628820, 34012224, 108413964, 344373768, 1090516932, 3443737680, 10847773692, 34093003032, 106928054964, 334731302496, 1046035320300, 3263630199336, 10167463313316, 31632108085872
Offset: 1
a(2) = 4 because in the 9 ternary words of length 2, namely 00, 01, 02, 10, 11, 12, 20, 21 and 22, we have altogether 4 isolated 0's.
A120925
Number of ternary words on {0,1,2} having no isolated 0's.
Original entry on oeis.org
1, 2, 5, 13, 33, 83, 209, 527, 1329, 3351, 8449, 21303, 53713, 135431, 341473, 860983, 2170865, 5473575, 13800961, 34797463, 87737617, 221219847, 557779233, 1406373239, 3546000945, 8940814823, 22543189057, 56839939415, 143315069777
Offset: 0
a(2)=5 because we have 00,11,12,21 and 22.
- Michael De Vlieger, Table of n, a(n) for n = 0..2490
- D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 11.
- Maksym Druchok, Volodymyr Krasnov, Taras Krokhmalskii, and Oleg Derzhko, One-dimensionally confined ammonia molecules: A theoretical study, arXiv:2307.06186 [cond-mat.stat-mech], 2023. See p. 5.
- Index entries for linear recurrences with constant coefficients, signature (3,-2,2).
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a[0]:=1:a[1]:=2:a[2]:=5: for n from 3 to 32 do a[n]:=3*a[n-1]-2*a[n-2]+2*a[n-3] od: seq(a[n],n=0..32);
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nn=20;a=x^2/(1-x);CoefficientList[Series[(a+1)/(1-(2x a)/(1-2x))/(1-2x),{x,0,nn}],x] (* Geoffrey Critzer, Jan 13 2013 *)
LinearRecurrence[{3,-2,2},{1,2,5},30] (* Harvey P. Dale, Nov 16 2024 *)
Showing 1-2 of 2 results.
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