25509168

Appears in sequences

• Number of ternary trees (A001764) with n nodes and maximal diameter.at n=14A064017
• Number of spanning trees on the bipartite graph K_{3,n}.at n=12A069996
• Numbers k such that Sum_{i=1..k} gcd(k,i) divides Sum_{i=1..k} lcm(k,i).at n=32A072109
• Horadam sequence (0,1,9,3).at n=11A085504
• a(n) = 3^(n-1)*Fibonacci(n).at n=12A099012
• a(n) = 3*a(n-1) + 9*a(n-2) for n > 1, with a(0)=1, a(1)=3.at n=11A122069
• One quarter the number of nX3 1..4 arrays with no two neighbors of any element equal to each other.at n=12A183355
• a(n) = (n/4)*3^(n/2)*((1+sqrt(3))^2+(-1)^n*(1-sqrt(3))^2).at n=24A187273
• Number of 3Xn binary arrays without the pattern 0 1 diagonally or antidiagonally.at n=14A188825
• Number of (n+1)X2 0..1 arrays with the number of clockwise edge increases in every 2X2 subblock differing from each horizontal or vertical neighbor.at n=26A205187
• T(n,k)=Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph.at n=34A223692
• Petersen graph (8,2) coloring a rectangular array: number of 7Xn 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph.at n=1A223698
• Denominators of mass formula for connected vacuum graphs on n nodes for a phi^4 field theory.at n=24A226259
• Expansion of (1+3*x)^2/(1-3*x)^2.at n=12A236967
• a(1) = 1, a(2) = 2, a(3) = 5; thereafter a(n) = 2 * Sum_{k=1..n-1} a(k).at n=16A257970
• a(n) = if n mod 6 = 0 then 4*3^((n-6)/3) elif n mod 6 = 1 then 2^4*3^((n-10)/3) elif n mod 6 = 2 then 2^3*3^((n-8)/3) elif n mod 6 = 3 then 2^2*3^((n-6)/3) elif n mod 6 = 4 then 2*3^((n-4)/3) otherwise 3^((n-2)/3).at n=41A276403
• Number of permutation polynomials (mod n).at n=26A329812