This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
The array starts in row n=0 with columns k>=0 as: 0 1 3 9 27 81 243 729 2187 ... A140429; 1 2 6 18 54 162 486 1458 4374 ... A025192; 1 4 12 36 108 324 972 2916 8748 ... A003946; 3 8 24 72 216 648 1944 5832 17496 ... A080923; 5 16 48 144 432 1296 3888 11664 34992 ... A257970; 11 32 96 288 864 2592 7776 23328 69984 ... 21 64 192 576 1728 5184 15552 46656 139968 ... Antidiagonal triangle begins as: 0; 1, 1; 1, 2, 3; 3, 4, 6, 9; 5, 8, 12, 18, 27; 11, 16, 24, 36, 54, 81; 21, 32, 48, 72, 108, 162, 243; 43, 64, 96, 144, 216, 324, 486, 729; 85, 128, 192, 288, 432, 648, 972, 1458, 2187; - _G. C. Greubel_, Mar 25 2021
t:= func< n,k | k eq 0 select (2^(n-k) -(-1)^(n-k))/3 else 2^(n-k)*3^(k-1) >; [t(n,k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 25 2021
T:=proc(n,k)if(k>0)then return 2^n*3^(k-1):else return (2^n - (-1)^n)/3:fi:end: for d from 0 to 8 do for m from 0 to d do print(T(d-m,m)):od:od: # Nathaniel Johnston, Apr 13 2011
t[n_, k_]:= If[k==0, (2^(n-k) -(-1)^(n-k))/3, 2^(n-k)*3^(k-1)];
Table[t[n, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Mar 25 2021 *)
def A155118(n,k): return (2^(n-k) -(-1)^(n-k))/3 if k==0 else 2^(n-k)*3^(k-1) flatten([[A155118(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 25 2021
Comments