cp's OEIS Frontend

A194480 T(n,k) = number of ways to arrange k indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.

%I A194480 #12 Mar 10 2023 10:04:30
%S A194480 1,0,3,0,3,6,0,1,15,10,0,0,17,45,15,0,0,6,105,105,21,0,0,0,114,410,
%T A194480 210,28,0,0,0,39,879,1225,378,36,0,0,0,1,909,4284,3066,630,45,0,0,0,0,
%U A194480 337,8568,15729,6762,990,55,0,0,0,0,15,8733,50526,47565,13560,1485,66,0,0,0
%N A194480 T(n,k) = number of ways to arrange k indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.
%C A194480 Table starts
%C A194480 ...1....0......0........0.........0..........0...........0............0
%C A194480 ...3....3......1........0.........0..........0...........0............0
%C A194480 ...6...15.....17........6.........0..........0...........0............0
%C A194480 ..10...45....105......114........39..........1...........0............0
%C A194480 ..15..105....410......879.......909........337..........15............0
%C A194480 ..21..210...1225.....4284......8568.......8733........3525..........285
%C A194480 ..28..378...3066....15729.....50526......96478.......98473........43713
%C A194480 ..36..630...6762....47565....221508.....668028.....1237434......1279905
%C A194480 ..45..990..13560...124803....789453....3413828.....9821400.....17860056
%C A194480 ..55.1485..25245...293733...2412333...14054915....57367112....159352995
%C A194480 ..66.2145..44275...634293...6542316...49171641...268378248...1046727933
%C A194480 ..78.3003..73931..1277133..16127397..151422970..1059987987...5488359255
%C A194480 ..91.4095.118482..2426424..36762726..420674150..3661533037..24183257037
%C A194480 .105.5460.183365..4389567..78495417.1073422309.11341971885..92740471038
%C A194480 .120.7140.275380..7615062.158548572.2550004472.32090198922.317395080927
%C A194480 .136.9180.402900.12739902.305303544.5699074284.84099053568.987664967535
%H A194480 R. H. Hardin, <a href="/A194480/b194480.txt">Table of n, a(n) for n = 1..290</a>
%H A194480 Manuel Kauers and Christoph Koutschan, <a href="https://arxiv.org/abs/2303.02793">Some D-finite and some Possibly D-finite Sequences in the OEIS</a>, arXiv:2303.02793 [cs.SC], 2023, pp. 31-33.
%F A194480 Empirical: T(n,k) is a polynomial of degree 2k in n with lead coefficient 1/(2^k*k!) for k <= 5.
%F A194480 T(n,1) = (1/2)*n^2 + (1/2)*n
%F A194480 T(n,2) = (1/8)*n^4 + (1/4)*n^3 - (1/8)*n^2 - (1/4)*n
%F A194480 T(n,3) = (1/48)*n^6 + (1/16)*n^5 - (3/16)*n^4 + (1/48)*n^3 + (1/6)*n^2 - (1/12)*n
%F A194480 T(n,4) = (1/384)*n^8 + (1/96)*n^7 - (5/64)*n^6 + (13/240)*n^5 + (27/128)*n^4 - (23/96)*n^3 - (13/96)*n^2 + (7/40)*n
%F A194480 T(n,5) = (1/3840)*n^10 + (1/768)*n^9 - (7/384)*n^8 + (37/1920)*n^7 + (737/3840)*n^6 - (2347/3840)*n^5 + (101/192)*n^4 + (93/320)*n^3 - (7/10)*n^2 + (3/10)*n
%e A194480 Some solutions for n=4, k=4:
%e A194480 .....1........0........0........0........0........0........1........1
%e A194480 ....1.0......1.0......0.1......0.1......1.0......1.1......0.1......0.1
%e A194480 ...0.1.0....1.0.1....0.1.0....0.0.1....0.1.1....0.1.0....1.1.0....0.1.0
%e A194480 ..0.0.0.1..0.0.0.1..1.0.1.0..0.1.1.0..0.0.0.1..1.0.0.0..0.0.0.0..0.0.1.0
%Y A194480 Column 1 is A000217.
%Y A194480 Column 2 is A050534(n+1).
%K A194480 nonn,tabl
%O A194480 1,3
%A A194480 _R. H. Hardin_, Aug 26 2011