OFFSET
1,2
COMMENTS
The sequences a_k(n) = T(n,k) are self-inverse permutations of the natural numbers:
T(n,1) = A054429(n);
T(n,2) = A115303(n-1) for n>1;
T(n,3) = A115304(n-2) for n>2;
T(n,4) = A115305(n-3) for n>3;
T(n,5) = A115306(n-4) for n>4;
T(n,6) = A115307(n-5) for n>5;
T(n,7) = A115308(n-6) for n>6;
T(n,8) = A115309(n-7) for n>7;
T(n,9) = A106649(n-8) for n>8;
T(n,k) = n-k+1 for k > n/2, especially T(n,n)=1 and T(2*n-1,n)=n.
LINKS
EXAMPLE
Triangle begins:
1;
3, 1;
2, 2, 1;
7, 5, 2, 1;
6, 4, 3, 2, 1;
5, 3, 7, 3, 2, 1;
4, 8, 6, 4, 3, 2, 1;
...
MATHEMATICA
T[n_, k_] := T[n, k] = If[n < 2 k, n - k + 1, (k + 1)*T[k - 1 + Floor[(n - k + 1)/(k + 1)], k] + k - Mod[n - k + 1, k + 1]];
Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 03 2021 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Jan 20 2006
STATUS
approved