A161380 Triangle read by rows: T(n,k) = 2*k*T(n-1,n-1) + 1 (n >= 0, 0 <= k <= n), with T(0,0) = 1.
1, 1, 3, 1, 7, 13, 1, 27, 53, 79, 1, 159, 317, 475, 633, 1, 1267, 2533, 3799, 5065, 6331, 1, 12663, 25325, 37987, 50649, 63311, 75973, 1, 151947, 303893, 455839, 607785, 759731, 911677, 1063623, 1, 2127247, 4254493, 6381739, 8508985, 10636231
Offset: 0
Examples
Triangle begins: 1 1 3 1 7 13 1 27 53 79 1 159 317 475 633 1 1267 2533 3799 5065 6331
Links
- Nathaniel Johnston, Table of n, a(n) for n = 0..2500
- Mathieu Guay-Paquet and Jeffrey Shallit, Avoiding Squares and Overlaps Over the Natural Numbers, arXiv:0901.1397 [math.CO], 2009.
- Mathieu Guay-Paquet and Jeffrey Shallit, Avoiding Squares and Overlaps Over the Natural Numbers. Discrete Math., 309 (2009), 6245-6254.
Programs
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Maple
T := proc(n,k) option remember: if(n=0 and k=0)then return 1: else return 2*k*T(n-1,n-1)+1: fi: end: for n from 0 to 8 do for k from 0 to n do printf("%d, ",T(n,k)): od: od: # Nathaniel Johnston, Apr 26 2011 -
Mathematica
T[0, 0] = 1; T[n_, k_] := 2*k*T[n - 1, n - 1] + 1; Table[Table[T[n, k], {k, 0, n}], {n, 0, 8}] // Flatten (* Jean-François Alcover, Nov 25 2017 *)