cp's OEIS Frontend

A359971 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.

%I A359971 #23 Jan 30 2023 10:32:59
%S A359971 1,5,33,15,108,126,5,727,1031,38,2,1314,2452,167,15,2,6811,12102,988,
%T A359971 52,14904,27626,3255,214,4,2,2,39172,73289,10062,795,19,1,65833,
%U A359971 127951,18476,1464,64,5,201643,370880,59630,5548,250,7,2,288196,541258,91037,9692,428,20,4,741597,1351301,239180,27510,1434,58
%N A359971 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.
%C A359971 The number of vertices along the shorter edges is A005728(n).
%C A359971 No formula for a(n) is known. The sequence is inspired by the Farey fan; see A360042.
%C A359971 See A359968 and A359969 for images of the triangle.
%e A359971 The table begins:
%e A359971         1;
%e A359971         5;
%e A359971        33,      15;
%e A359971       108,     126,      5;
%e A359971       727,    1031,     38,     2;
%e A359971      1314,    2452,    167,    15,    2;
%e A359971      6811,   12102,    988,    52;
%e A359971     14904,   27626,   3255,   214,    4,   2, 2;
%e A359971     39172,   73289,  10062,   795,   19,   1;
%e A359971     65833,  127951,  18476,  1464,   64,   5;
%e A359971    201643,  370880,  59630,  5548,  250,   7, 2;
%e A359971    288196,  541258,  91037,  9692,  428,  20, 4;
%e A359971    741597, 1351301, 239180, 27510, 1434,  58;
%e A359971   1095197, 2025237, 374907, 44880, 2491, 104, 4, 2;
%e A359971   1747260, 3279178, 628335, 76787, 4600, 178, 6;
%e A359971   ...
%Y A359971 Cf. A359968 (vertices), A359969 (regions and row sums), A359970 (edges), A005728, A360042, A359977, A359694, A358951, A358889.
%K A359971 nonn,tabf
%O A359971 1,2
%A A359971 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 20 2023