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 A361789 #8 Mar 26 2023 10:30:00 %S A361789 0,1,1,2,1,2,3,3,3,3,4,3,2,3,4,5,4,3,3,4,5,6,6,6,3,6,6,6,7,6,5,6,6,5, %T A361789 6,7,8,8,6,6,4,6,6,8,8,9,8,7,6,6,6,6,7,8,9,10,9,8,8,6,5,6,8,8,9,10,11, %U A361789 11,11,8,11,6,6,11,8,11,11,11,12,11,10,11,11,10,6,10,11,11,10,11,12 %N A361789 A(n, k) is the sum of the distinct terms in the dual Zeckendorf representations of n or of k; square array A(n, k) read by antidiagonals, n, k >= 0. %C A361789 The dual Zeckendorf representation corresponds to the lazy Fibonacci representation (see A356771 for further details). %H A361789 Rémy Sigrist, <a href="/A361789/a361789.png">Colored representation of the table for x, y < Fibonacci(16) - 1</a> (where the color is function of A(x, y)) %H A361789 Rémy Sigrist, <a href="/A361789/a361789.gp.txt">PARI program</a> %H A361789 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a> %F A361789 A(n, k) = A022290(A003754(n+1) OR A003754(k+1)) (where OR denotes the bitwise OR operator, A004198). %F A361789 A(n, k) = A(k, n). %F A361789 A(n, 0) = n. %F A361789 A(n, n) = n. %F A361789 A(A(m, n), k) = A(m, A(n, k)). %F A361789 A(A(n, k), n) = A(n, k). %F A361789 A(n, A361756(n, k)) = n. %e A361789 Array A(n, k) begins: %e A361789 n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 %e A361789 ----+------------------------------------------------------- %e A361789 0 | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 %e A361789 1 | 1 1 3 3 4 6 6 8 8 9 11 11 12 14 %e A361789 2 | 2 3 2 3 6 5 6 7 8 11 10 11 14 13 %e A361789 3 | 3 3 3 3 6 6 6 8 8 11 11 11 14 14 %e A361789 4 | 4 4 6 6 4 6 6 11 11 9 11 11 12 14 %e A361789 5 | 5 6 5 6 6 5 6 10 11 11 10 11 14 13 %e A361789 6 | 6 6 6 6 6 6 6 11 11 11 11 11 14 14 %e A361789 7 | 7 8 7 8 11 10 11 7 8 11 10 11 19 18 %e A361789 8 | 8 8 8 8 11 11 11 8 8 11 11 11 19 19 %e A361789 9 | 9 9 11 11 9 11 11 11 11 9 11 11 17 19 %e A361789 10 | 10 11 10 11 11 10 11 10 11 11 10 11 19 18 %e A361789 11 | 11 11 11 11 11 11 11 11 11 11 11 11 19 19 %e A361789 12 | 12 12 14 14 12 14 14 19 19 17 19 19 12 14 %e A361789 13 | 13 14 13 14 14 13 14 18 19 19 18 19 14 13 %o A361789 (PARI) See Links section. %Y A361789 Cf. A003754, A003986, A022290, A334348, A356771, A356969, A361756. %K A361789 nonn,base,tabl %O A361789 0,4 %A A361789 _Rémy Sigrist_, Mar 24 2023