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A265903 Square array read by descending antidiagonals: A(1,k) = A188163(k), and for n > 1, A(n,k) = A087686(1+A(n-1,k)).

%I A265903 #39 Sep 20 2016 13:24:50
%S A265903 1,3,2,5,7,4,6,12,15,8,9,14,27,31,16,10,21,30,58,63,32,11,24,48,62,
%T A265903 121,127,64,13,26,54,106,126,248,255,128,17,29,57,116,227,254,503,511,
%U A265903 256,18,38,61,120,242,475,510,1014,1023,512,19,42,86,125,247,496,978,1022,2037,2047,1024,20,45,96,192,253,502,1006,1992,2046,4084,4095,2048
%N A265903 Square array read by descending antidiagonals: A(1,k) = A188163(k), and for n > 1, A(n,k) = A087686(1+A(n-1,k)).
%C A265903 Square array A(n,k) [where n is row and k is column] is read by descending antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
%C A265903 For n >= 3, each row n lists the numbers that appear n times in A004001. See also A051135.
%H A265903 Antti Karttunen, <a href="/A265903/b265903.txt">Table of n, a(n) for n = 1..210; the first 20 antidiagonals of array</a>
%H A265903 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%H A265903 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A265903 For the first row n=1, A(1,k) = A188163(k), for rows n > 1, A(n,k) = A087686(1+A(n-1,k)).
%e A265903 The top left corner of the array:
%e A265903      1,    3,    5,    6,     9,    10,    11,    13,    17,    18,    19
%e A265903      2,    7,   12,   14,    21,    24,    26,    29,    38,    42,    45
%e A265903      4,   15,   27,   30,    48,    54,    57,    61,    86,    96,   102
%e A265903      8,   31,   58,   62,   106,   116,   120,   125,   192,   212,   222
%e A265903     16,   63,  121,  126,   227,   242,   247,   253,   419,   454,   469
%e A265903     32,  127,  248,  254,   475,   496,   502,   509,   894,   950,   971
%e A265903     64,  255,  503,  510,   978,  1006,  1013,  1021,  1872,  1956,  1984
%e A265903    128,  511, 1014, 1022,  1992,  2028,  2036,  2045,  3864,  3984,  4020
%e A265903    256, 1023, 2037, 2046,  4029,  4074,  4083,  4093,  7893,  8058,  8103
%e A265903    512, 2047, 4084, 4094,  8113,  8168,  8178,  8189, 16006, 16226, 16281
%e A265903   1024, 4095, 8179, 8190, 16292, 16358, 16369, 16381, 32298, 32584, 32650
%e A265903   ...
%o A265903 (Scheme)
%o A265903 (define (A265903 n) (A265903bi (A002260 n) (A004736 n)))
%o A265903 (define (A265903bi row col) (if (= 1 row) (A188163 col) (A087686 (+ 1 (A265903bi (- row 1) col)))))
%Y A265903 Inverse permutation: A267104.
%Y A265903 Transpose: A265901.
%Y A265903 Row 1: A188163.
%Y A265903 Row 2: A266109.
%Y A265903 Row 3: A267103.
%Y A265903 For the known and suspected columns, see the rows listed for transposed array A265901.
%Y A265903 Cf. A004001, A051135, A087686.
%Y A265903 Cf. A265900 (main diagonal), A265909 (submain diagonal).
%Y A265903 Cf. A162598 (column index of n in array), A265332 (row index of n in array).
%Y A265903 Cf. also permutations A267111, A267112.
%K A265903 nonn,tabl
%O A265903 1,2
%A A265903 _Antti Karttunen_, Dec 18 2015