OFFSET
0,10
COMMENTS
See David et al. link for definitions.
LINKS
Robert Davis, Sarah A. Nelson, T. Kyle Petersen, Bridget E. Tenner, The pinnacle set of a permutation, arXiv:1704.05494 [math.CO], 2017.
FORMULA
T(n,k) = Sum_{n>2k} T(n,k-1) if n>2*k; T(n,k) = 0 if n<=2*k; T(0,0) = 1.
EXAMPLE
Triangle begins:
1;
0;
0;
0, 1;
0, 1;
0, 1, 2;
0, 1, 3;
0, 1, 4, 5;
0, 1, 5, 9;
...
MATHEMATICA
T[0, 0] = 1; T[_, 0] = 0; T[n_, k_] /; n <= 2k = 0; T[n_, k_] := T[n, k] = Sum[T[j, k-1], {j, 0, n-1}];
Table[T[n, k], {n, 0, 16}, {k, 0, Max[0, (n-1)/2]}] // Flatten (* Jean-François Alcover, Feb 02 2019 *)
PROG
(PARI) T(n, k) = {if ((n==0) && (k==0), return (1)); if (n <= 2*k, return(0)); sum(kk=0, n-1, T(kk, k-1)); }
tabf(nn) = {print(T(0, 0), ", "); for (n=1, nn, for (k=0, round(n-1)\2, print1(T(n, k), ", "); ); print(); ); }
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Michel Marcus, Jul 14 2017
STATUS
approved