cp's OEIS Frontend

A341695 Regular triangle read by rows, T(n,k) = T(n,k-1)+2*T(n-1,k)-T(n-1,k-1) for 1<=k<=n-2 with T(n,n)=T(n,n-1)=T(n,n-2) for n>=3 and T(1,1)=T(2,1)=T(2,2)=1.

%I A341695 #49 Jun 02 2024 11:00:10
%S A341695 1,1,1,2,2,2,4,6,6,6,8,16,22,22,22,16,40,68,90,90,90,32,96,192,304,
%T A341695 394,394,394,64,224,512,928,1412,1806,1806,1806,128,512,1312,2656,
%U A341695 4552,6752,8558,8558,8558,256,1152,3264,7264,13712,22664,33028,41586,41586,41586
%N A341695 Regular triangle read by rows, T(n,k) = T(n,k-1)+2*T(n-1,k)-T(n-1,k-1) for 1<=k<=n-2 with T(n,n)=T(n,n-1)=T(n,n-2) for n>=3 and T(1,1)=T(2,1)=T(2,2)=1.
%H A341695 Dongsu Kim and Zhicong Lin, <a href="https://arxiv.org/abs/1706.07208">Refined restricted inversion sequences</a>, arXiv:1706.07208 [math.CO], 2017-2020.
%H A341695 Toufik Mansour and Mark Shattuck, <a href="https://arxiv.org/abs/2104.04491">On a conjecture of Lin and Kim concerning a refinement of Schröder numbers</a>, arXiv:2104.04491 [math.CO], 2021.
%e A341695 Triangle begins:
%e A341695    1;
%e A341695    1,  1;
%e A341695    2,  2,  2;
%e A341695    4,  6,  6,  6;
%e A341695    8, 16, 22, 22, 22;
%e A341695   16, 40, 68, 90, 90, 90;
%e A341695   ...
%o A341695 (PARI)
%o A341695 T(n,k) = if (k>=1, if (n<=2, 1, if (k<=n-2, T(n,k-1)+2*T(n-1,k)-T(n-1,k-1), T(n,n-2))));
%o A341695 tabl(nn) = {for (n=1, nn, for (k=1, n, print1(T(n,k), ", ");); print;);}
%Y A341695 Cf. A011782 (1st column), A155069 (right diagonal).
%K A341695 nonn,tabl,easy
%O A341695 1,4
%A A341695 _Michel Marcus_, Apr 12 2021