A342167
a(n) = U(n, (n+2)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.
Original entry on oeis.org
1, 3, 15, 115, 1189, 15456, 242047, 4435929, 93149001, 2205405829, 58130412911, 1688353631328, 53577891882061, 1844491975179855, 68470281953483775, 2726406212682669391, 115921586524134874897, 5241862216131004082160, 251197634537351883217999
Offset: 0
- Seiichi Manyama, Table of n, a(n) for n = 0..386
- Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, Metered Parking Functions, arXiv:2406.12941 [math.CO], 2024. See pp. 11, 22.
- Wikipedia, Chebyshev polynomials.
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Table[ChebyshevU[n, (n + 2)/2], {n, 0, 18}] (* Amiram Eldar, Apr 27 2021 *)
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a(n) = polchebyshev(n, 2, (n+2)/2);
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a(n) = sum(k=0, n, n^(n-k)*binomial(2*n+1-k, k));
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a(n) = sum(k=0, n, n^k*binomial(n+1+k, 2*k+1));
A372817
Table read by antidiagonals: T(m,n) = number of 1-metered (m,n)-parking functions.
Original entry on oeis.org
1, 0, 2, 0, 3, 3, 0, 4, 8, 4, 0, 6, 21, 15, 5, 0, 8, 55, 56, 24, 6, 0, 12, 145, 209, 115, 35, 7, 0, 16, 380, 780, 551, 204, 48, 8, 0, 24, 1000, 2912, 2640, 1189, 329, 63, 9, 0, 32, 2625, 10868, 12649, 6930, 2255, 496, 80, 10, 0, 48, 6900, 40569, 60606, 40391, 15456, 3905, 711, 99, 11
Offset: 1
For T(3,2) the 1-metered (3,2)-parking functions are 111, 121, 211, 212.
Table begins:
1, 2, 3, 4, 5, 6, 7, ...
0, 3, 8, 15, 24, 35, 48, ...
0, 4, 21, 56, 115, 204, 329, ...
0, 6, 55, 209, 551, 1189, 2255, ...
0, 8, 145, 780, 2640, 6930, 15456, ...
0, 12, 380, 2912, 12649, 40391, 105937, ...
0, 16, 1000, 10868, 60606, 235416, 726103, ...
...
- Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, Metered Parking Functions, arXiv:2406.12941 [math.CO], 2024.
A342207
a(n) = U(n,n+1) where U(n,x) is a Chebyshev polynomial of the second kind.
Original entry on oeis.org
1, 4, 35, 496, 9701, 241956, 7338631, 262184896, 10783446409, 501827040100, 26069206375211, 1495427735314800, 93885489910449901, 6403169506981578436, 471427031236487965199, 37265225545829174607616, 3147895910861898495432209
Offset: 0
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Table[ChebyshevU[n, n + 1], {n, 0, 16}] (* Amiram Eldar, Mar 05 2021 *)
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a(n) = polchebyshev(n, 2, n+1);
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a(n) = sum(k=0, n, (2*n)^(n-k)*binomial(2*n+1-k, k));
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a(n) = sum(k=0, n, (2*n)^k*binomial(n+1+k, 2*k+1));
A384162
Number of length n words over an n-ary alphabet such that a single letter in every run of letters is marked.
Original entry on oeis.org
1, 6, 45, 460, 5945, 92736, 1694329, 35487432, 838341009, 22054058290, 639434542021, 20260243575936, 696512594466793, 25822887652517970, 1027054229302256625, 43622499402922710256, 1970666970910292873249, 94353519890358073478880, 4772755056209685781141981
Offset: 1
a(2) = 6 counts: (1#,1), (1,1#), (1#,2#), (2#,1#), (2#,2), (2,2#) where # denotes a mark.
Showing 1-4 of 4 results.