A361575 - OEIS

%I #8 Mar 30 2023 09:17:07

%S 1,3,5,11,13,30,34,71,97,177,233,481,610,1157,1677,3027,4181,8016,

%T 10946,20379,29534,52461,75025,140748,196778,355979,526123,933044,

%U 1346269,2469992,3524578,6342729,9400985,16487211

%N Number of Fibonacci meanders of length n.

%C For an overview of the terms and functions used, compare A361574. The corresponding sequence counting meanders without the requirement to be Fibonacci is A199932.

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/FibonacciMeanders">Fibonacci meanders</a>.

%e Fibonacci meanders with length 6 can have the central angle 360/m, where m is in divisors(6) = {1, 2, 3, 6}. In total there are a(6) = 30 such meanders, the list shows their binary representation together with the multiplicity with which they appear.

%e 100000 x 1, 100001 x 2, 100010 x 1, 100100 x 2, 100101 x 1, 101000 x 1,

%e 101001 x 1, 101010 x 1, 110000 x 2, 110001 x 2, 110010 x 1, 110100 x 1,

%e 110101 x 1, 111000 x 2, 111001 x 2, 111010 x 1, 111100 x 2, 111101 x 1,

%e 111110 x 1, 111111 x 4.

%p # The list A was computed with the functions given in A361574. They correspond to the columns in the table shown in the reference.

%p A := [[1, 2, 4, 7, 12, 20, 33, 54, 88, 143, 232, 376, 609, 986, 1596, 2583, 4180, 6764, 10945, 17710, 28656, 46367, 75024, 121392, 196417, 317810, 514228, 832039, 1346268, 2178308, 3524577, 5702886, 9227464, 14930351], [1, 3, 6, 13, 30, 70, 167, 405, 992, 2450, 6090, 15214, 38165, 96069, 242530, 613811, 1556856], [1, 3, 8, 21, 68, 242, 861, 3151, 11874, 45192, 173496], [1, 3, 10, 35, 154, 858, 4723, 25625], [1, 3, 12, 61, 360, 3058], [1, 3, 14, 111, 878], [1, 3, 16, 209], [1, 3, 18, 403], [1, 3, 20], [1, 3, 22], [1, 3, 24], [1, 3], [1, 3], [1, 3], [1, 3], [1, 3], [1, 3], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]];

%p with(LinearAlgebra):  # a(n) is the sum of row n of this table.

%p row := k -> [seq(`if`(irem(n, k) <> 0, 0, A[k][n/k]), n = 1..34)]:

%p M := Transpose(Matrix([seq(row(n), n = 1..34)])):

%p seq(add(m, m = Row(M, n)), n = 1..34);

%Y Cf. A361574, A199932, A198060.

%K nonn,more

%O 1,2

%A _Peter Luschny_, Mar 16 2023