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T13

T_{13}(n,k) = \genfrac{\{}{.}{0pt}{}{T(0,0) \leftarrow 1, T(n,n)\leftarrow T(n-1,0)}{T(n,k)\leftarrow T(n,k+1)+T(n-1,k)}

TriangleForm
1  
1 2  
2 3 5  
5 7 10 15  
15 20 27 37 52  
52 67 87 114 151 203  
203 255 322 409 523 674 877
sum als gcd lcm
1 1 0 1
3 1 2 2
10 4 1 30
37 7 1 210
151 37 1 259740
674 94 1 6087317964
3263 587 1 150538831664272170
RectangleForm
1 1 2 5 15 52 203
2 3 7 20 67 255 1080
5 10 27 87 322 1335 6097
15 37 114 409 1657 7432 36401
52 151 523 2066 9089 43833 229114
203 674 2589 11155 52922 272947 1515903
877 3263 13744 64077 325869 1788850 10515147
Fingerprint
SubSeqType 0 1 2 3
Row A000110 A011968 A011969 A011970
Column A000110 A005493 A011965 A011966
DiagRow A094577 A000000 A000000 A000000
DiagColumn A094577 A020556 A000000 A000000
Characteristic SUM ALS LCM GCD
Sequence A005493 A000000 A000000 A000012

Maple T13 := proc(n, k) if n = 0 and k = 0 then 1 elif k = n then T13(n-1, 0) else T13(n, k + 1) + T13(n - 1, k) fi end:

TeX T_{13}(n,k) = \genfrac{\{}{.}{0pt}{}{T(0,0) \leftarrow 1, T(n,n)\leftarrow T(n-1,0)}{T(n,k)\leftarrow T(n,k+1)+T(n-1,k)}