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 A135090 #14 Mar 21 2024 06:00:19
%S A135090 0,0,0,0,3,0,0,5,5,0,0,8,8,8,0,0,11,13,13,11,0,0,13,18,21,18,13,0,0,
%T A135090 16,21,29,29,21,16,0,0,18,26,34,40,34,26,18,0,0,21,29,42,47,47,42,29,
%U A135090 21,0,0,24,34,47,58,55,58,47,34,24,0,0,26,39,55,65,68,68,65,55,39,26,0,0,29,42,63,76,76,84,76,76,63,42,29,0,0,32,47
%N A135090 Array read by antidiagonals: T(n, k) = Knuth's Fibonacci (or circle) product of n and k ("n o k"), n >= 0, k >= 0.
%C A135090 This is a variant of A101330. See that entry for much more information.
%H A135090 Paolo Xausa, <a href="/A135090/b135090.txt">Table of n, a(n) for n = 0..11324</a> (first 150 antidiagonals, flattened).
%F A135090 T(n, k) = 3*n*k - n*h(k) - k*h(n) where h(n) = A060144(n + 1). - _Peter Luschny_, Mar 21 2024
%e A135090 Array begins:
%e A135090 n\k | 0 1 2 3 4 5 6 7 8 9 ...
%e A135090 ----+------------------------------------------------
%e A135090 0 | 0 0 0 0 0 0 0 0 0 0 ...
%e A135090 1 | 0 3 5 8 11 13 16 18 21 24 ...
%e A135090 2 | 0 5 8 13 18 21 26 29 34 39 ...
%e A135090 3 | 0 8 13 21 29 34 42 47 55 63 ...
%e A135090 4 | 0 11 18 29 40 47 58 65 76 87 ...
%e A135090 5 | 0 13 21 34 47 55 68 76 89 102 ...
%e A135090 6 | 0 16 26 42 58 68 84 94 110 126 ...
%e A135090 7 | 0 18 29 47 65 76 94 105 123 141 ...
%e A135090 8 | 0 21 34 55 76 89 110 123 144 165 ...
%e A135090 9 | 0 24 39 63 87 102 126 141 165 189 ...
%e A135090 ...
%p A135090 h := n -> floor(2*(n + 1)/(sqrt(5) + 3)): # A060144(n+1)
%p A135090 T := (n, k) -> 3*n*k - n*h(k) - k*h(n):
%p A135090 seq(print(seq(T(n, k), k = 0..9)), n = 0..7); # _Peter Luschny_, Mar 21 2024
%t A135090 A135090[n_, k_] := 3*n*k - n*Floor[(k + 1) / GoldenRatio^2] - k*Floor[(n + 1) / GoldenRatio^2];
%t A135090 Table[A135090[n-k, k], {n, 0, 15}, {k, 0, n}] (* _Paolo Xausa_, Mar 21 2024 *)
%Y A135090 Cf. A101330, A060144, A001622.
%K A135090 nonn,tabl
%O A135090 0,5
%A A135090 _N. J. A. Sloane_, May 17 2008