A255813
Numbers of words on {0,1,2,3} having no isolated zeros.
Original entry on oeis.org
1, 3, 10, 34, 115, 388, 1309, 4417, 14905, 50296, 169720, 572707, 1932556, 6521263, 22005505, 74255899, 250570870, 845532298, 2853184279, 9627852832, 32488455385, 109629815881, 369937455865, 1248325741972, 4212380047936
Offset: 0
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- 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.
- Index entries for linear recurrences with constant coefficients, signature (4,-3,3).
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RecurrenceTable[{a[0] == 1, a[1] == 3, a[2]== 10, a[n] == 4 a[n - 1] - 3 a[n - 2] + 3 a[n - 3]}, a[n], {n, 0, 25}]
LinearRecurrence[{4, -3, 3}, {1, 3, 10}, 100] (* G. C. Greubel, Jun 02 2016 *)
A255814
Numbers of words on {0,1,2,3,4,} having no isolated zeros.
Original entry on oeis.org
1, 4, 17, 73, 313, 1341, 5745, 24613, 105449, 451773, 1935521, 8292309, 35526553, 152205613, 652091089, 2793739205, 11969154121, 51279178141, 219694231041, 941231059125, 4032495084025, 17276328107789, 74016584439345, 317107590101669
Offset: 0
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- 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.
- Index entries for linear recurrences with constant coefficients, signature (5,-4,4).
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I:=[1,4,17]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+4*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 26 2018
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RecurrenceTable[{a[0] == 1, a[1] == 4, a[2]== 17, a[n] == 5 a[n - 1] - 4 a[n - 2] + 4 a[n - 3]}, a[n], {n, 0, 23}]
LinearRecurrence[{5, -4, 4}, {1, 4, 17}, 100] (* G. C. Greubel, Jun 02 2016 *)
CoefficientList[Series[(-1 + x - x^2) / (-1 + 5 x -4 x^2 + 4 x^3), {x, 0, 33}], x] (* Vincenzo Librandi, Feb 26 2018 *)
A255815
Numbers of words on {0,1,2,3,4,5} having no isolated zeros.
Original entry on oeis.org
1, 5, 26, 136, 711, 3716, 19421, 101501, 530481, 2772486, 14490016, 75730071, 395792776, 2068556381, 10811024761, 56502330541, 295301641346, 1543353319176, 8066123361031, 42156481777036, 220325040452941, 1151498450637621
Offset: 0
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- 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.
- Index entries for linear recurrences with constant coefficients, signature (6,-5,5).
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RecurrenceTable[{a[0] == 1, a[1] == 5, a[2]== 26, a[n] == 6 a[n - 1] - 5 a[n - 2] + 5 a[n - 3]}, a[n], {n, 0, 21}]
LinearRecurrence[{6, -5, 5}, {1, 5, 26}, 100] (* G. C. Greubel, Jun 02 2016 *)
A255821
Numbers of words on {0,1,...,36} having no isolated zeros.
Original entry on oeis.org
1, 36, 1297, 46729, 1683577, 60656797, 2185374961, 78735837637, 2836736138665, 102203420474269, 3682238546710945, 132665625592223221, 4779746882367738841, 172207232713967895181, 6204372685172893559377, 223534399861459456068709
Offset: 0
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RecurrenceTable[{a[0] == 1, a[1] == 36, a[2]== 1297, a[n] == 37 a[n - 1] - 36 a[n - 2] + 36 a[n - 3]}, a[n], {n, 0, 15}]
LinearRecurrence[{37,-36,36}, {1, 36, 1297}, 100] (* G. C. Greubel, Jun 02 2016 *)
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Vec(-(x^2-x+1)/(36*x^3-36*x^2+37*x-1) + O(x^100)) \\ Colin Barker, Mar 09 2015
Showing 1-4 of 4 results.
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