OFFSET
1,1
COMMENTS
For k >= 5 and n >= k, T(n, k) is the maximum number of induced copies of a cycle of length k in a n-vertex graph (see Král, Norin and Volec Theorem 1).
LINKS
Daniel Král, Sergey Norin and Jan Volec, A bound on the inducibility of cycles, arXiv:1801.01556 [math.CO], 2018; Journal of Combinatorial Theory, Series A, 161 (2019) 359-363.
EXAMPLE
n\k| 1 2 3 4 5 6 7 8 9 10
---+----------------------------------------
1 | 2
2 | 4 2
3 | 6 4 2
4 | 8 8 4 2
5 | 10 12 9 4 2
6 | 12 18 16 10 4 2
7 | 14 24 25 18 10 5 2
8 | 16 32 37 32 20 11 5 2
9 | 18 40 54 51 37 22 11 5 2
10 | 20 50 74 78 64 42 24 11 5 2
...
MAPLE
a := (n, k) -> floor(2*n^k/k^k): seq(seq(a(n, k), k = 1 .. n), n = 1 .. 20)
MATHEMATICA
Flatten[Table[Floor[2*n^k/k^k], {n, 1, 15}, {k, 1, n}]]
PROG
(Magma) [[Floor(2*n^k/k^k): k in [1..n]]: n in [1..10]]; // triangle output
(Maxima) sjoin(v, j) := apply(sconcat, rest(join(makelist(j, length(v)), v)))$ display_triangle(n) := for i from 1 thru n do disp(sjoin(makelist(floor(2*i^j/j^j), j, 1, i), " ")); display_triangle(10);
(PARI)
T(n, k) = floor(2*n^k/k^k);
tabl(nn) = for(i=1, nn, for(j=1, i, print1(T(i, j), ", ")); print);
tabl(10) \\ triangle output
(GAP) Flat(List([1..15], n->List([1..n], k->Int(2*n^k/k^k)))); # Muniru A Asiru, Nov 25 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Nov 25 2018
EXTENSIONS
a(71)-a(78) from Muniru A Asiru, Nov 25 2018
STATUS
approved