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