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.

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, 394, 394, 394, 64, 224, 512, 928, 1412, 1806, 1806, 1806, 128, 512, 1312, 2656, 4552, 6752, 8558, 8558, 8558, 256, 1152, 3264, 7264, 13712, 22664, 33028, 41586, 41586, 41586

Offset

1,4

Links

Table of n, a(n) for n=1..55.

Dongsu Kim and Zhicong Lin, Refined restricted inversion sequences, arXiv:1706.07208 [math.CO], 2017-2020.

Toufik Mansour and Mark Shattuck, On a conjecture of Lin and Kim concerning a refinement of Schröder numbers, arXiv:2104.04491 [math.CO], 2021.

Example

Triangle begins:
   1;
   1,  1;
   2,  2,  2;
   4,  6,  6,  6;
   8, 16, 22, 22, 22;
  16, 40, 68, 90, 90, 90;
  ...

Prog

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))));
tabl(nn) = {for (n=1, nn, for (k=1, n, print1(T(n, k), ", "); ); print; ); }

Crossrefs

Cf. A011782 (1st column), A155069 (right diagonal).

Sequence in context: A182539 A170887 A103265 * A008238 A218870 A264869

Adjacent sequences: A341692 A341693 A341694 * A341696 A341697 A341698

Keyword

nonn,tabl,easy

Author

Michel Marcus, Apr 12 2021

Status

approved