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.
%I A101385 #11 Mar 29 2016 10:38:35
%S A101385 3,8,8,21,34,21,24,144,144,24,55,152,987,152,55,58,610,1008,1008,610,
%T A101385 58,63,618,6765,1032,6765,618,63,144,644,6786,6820,6820,6786,644,144,
%U A101385 147,2584,6909,6844,75025,6844,6909,2584,147,152,2592,46368,6972,75080
%N A101385 Array read by antidiagonals: T(n,k) = variant of Knuth's Fibonacci (or circle) product of n and k (A101330).
%C A101385 Let n = Sum_{i >= 2} eps(i) Fib_i and k = Sum_{j >= 2} eps(j) Fib_j be the Zeckendorf expansions of n and k, respectively (cf. A035517, A014417). The product of n and k is defined here to be Sum_{i,j} eps(i)*eps(j) Fib_{i*j} (= T(n,k)).
%H A101385 D. E. Knuth, <a href="http://dx.doi.org/10.1016/0893-9659(88)90176-0">Fibonacci multiplication</a>, Appl. Math. Lett. 1 (1988), 57-60.
%e A101385 Array begins:
%e A101385 3 8 21 24 55 ...
%e A101385 8 34 144 152 ...
%e A101385 21 144 987 ...
%e A101385 24 152 ...
%e A101385 55 ...
%t A101385 zeck[n_Integer] := Block[{k = Ceiling[ Log[ GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[ fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k-- ]; FromDigits[fr]]; kfpv[n_, m_] := Block[{y = Reverse[ IntegerDigits[ zeck[ n]]], z = Reverse[ IntegerDigits[ zeck[ m]]]}, Sum[ y[[i]]*z[[j]]*Fibonacci[(i + 1)(j + 1)], {i, Length[y]}, {j, Length[z]}]]; (* _Robert G. Wilson v_, Feb 09 2005 *)
%t A101385 Flatten[ Table[ kfpv[i, n - i], {n, 2, 12}, {i, n - 1, 1, -1}]] (* _Robert G. Wilson v_, Feb 09 2005 *)
%Y A101385 Cf. A101330, A035517, A014417. Main diagonal is A101633.
%Y A101385 First 3 rows give A101643, A101644, A101645.
%K A101385 nonn,tabl,easy
%O A101385 1,1
%A A101385 _N. J. A. Sloane_, Jan 25 2005
%E A101385 More terms from _David Applegate_, Jan 26 2005