cp's OEIS Frontend

A289871 Irregular triangle read by rows T(n, k) is the number of admissible pinnacle sets with maximum element n and cardinality k.

%I A289871 #10 Feb 02 2019 10:29:21
%S A289871 1,0,0,0,1,0,1,0,1,2,0,1,3,0,1,4,5,0,1,5,9,0,1,6,14,14,0,1,7,20,28,0,
%T A289871 1,8,27,48,42,0,1,9,35,75,90,0,1,10,44,110,165,132,0,1,11,54,154,275,
%U A289871 297,0,1,12,65,208,429,572,429,0,1,13,77,273,637,1001,1001
%N A289871 Irregular triangle read by rows T(n, k) is the number of admissible pinnacle sets with maximum element n and cardinality k.
%C A289871 See David et al. link for definitions.
%H A289871 Robert Davis, Sarah A. Nelson, T. Kyle Petersen, Bridget E. Tenner, <a href="https://arxiv.org/abs/1704.05494">The pinnacle set of a permutation</a>, arXiv:1704.05494 [math.CO], 2017.
%F A289871 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.
%e A289871 Triangle begins:
%e A289871 1;
%e A289871 0;
%e A289871 0;
%e A289871 0, 1;
%e A289871 0, 1;
%e A289871 0, 1, 2;
%e A289871 0, 1, 3;
%e A289871 0, 1, 4, 5;
%e A289871 0, 1, 5, 9;
%e A289871 ...
%t A289871 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}];
%t A289871 Table[T[n, k], {n, 0, 16}, {k, 0, Max[0, (n-1)/2]}] // Flatten (* _Jean-François Alcover_, Feb 02 2019 *)
%o A289871 (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));}
%o A289871 tabf(nn) = {print(T(0, 0), ", "); for (n=1, nn, for (k=0, round(n-1)\2, print1(T(n, k), ", ");); print(););}
%Y A289871 Cf. A008315, A037952 (row sums).
%K A289871 nonn,tabf
%O A289871 0,10
%A A289871 _Michel Marcus_, Jul 14 2017