cp's OEIS Frontend

A255555 Square array A(row,col) read by downwards antidiagonals: A(1,1) = 1, A(row,1) = A055938(row-1), and for col > 1, A(row,col) = A005187(1+A(row,col-1)).

%I A255555 #20 Nov 30 2016 22:10:28
%S A255555 1,3,2,7,4,5,15,8,10,6,31,16,19,11,9,63,32,38,22,18,12,127,64,74,42,
%T A255555 35,23,13,255,128,146,82,70,46,25,14,511,256,290,162,138,89,49,26,17,
%U A255555 1023,512,578,322,274,176,97,50,34,20,2047,1024,1154,642,546,350,193,98,67,39,21,4095,2048,2306,1282,1090,695,385,194,134,78,41,24
%N A255555 Square array A(row,col) read by downwards antidiagonals: A(1,1) = 1, A(row,1) = A055938(row-1), and for col > 1, A(row,col) = A005187(1+A(row,col-1)).
%C A255555 The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
%C A255555 Provided that I understand Kimberling's terminology correctly, this array is the dispersion of sequence b(n) = A005187(n+1), for n>=1: A005187[2..] = [3, 4, 7, 8, 10, 11, ...]. The left column is the complement of that sequence, which is {1} followed by A055938. - _Antti Karttunen_, Apr 17 2015
%H A255555 Antti Karttunen, <a href="/A255555/b255555.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a>
%H A255555 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/intersp.html">Interspersions and Dispersions</a>.
%H A255555 Clark Kimberling, <a href="http://www.jstor.org/discover/10.2307/2159163">Interspersions and Dispersions</a>, Proceedings of the American Mathematical Society, 117 (1993) 313-321.
%H A255555 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A255555 A(1,1) = 1, A(row,1) = A055938(row-1), and for col > 1, A(row,col) = A005187(1+A(row,col-1)).
%e A255555 The top left corner of the array:
%e A255555    1,  3,  7,  15,  31,  63,  127,  255,  511, 1023,  2047,  4095
%e A255555    2,  4,  8,  16,  32,  64,  128,  256,  512, 1024,  2048,  4096
%e A255555    5, 10, 19,  38,  74, 146,  290,  578, 1154, 2306,  4610,  9218
%e A255555    6, 11, 22,  42,  82, 162,  322,  642, 1282, 2562,  5122, 10242
%e A255555    9, 18, 35,  70, 138, 274,  546, 1090, 2178, 4354,  8706, 17410
%e A255555   12, 23, 46,  89, 176, 350,  695, 1387, 2770, 5535, 11067, 22128
%e A255555   13, 25, 49,  97, 193, 385,  769, 1537, 3073, 6145, 12289, 24577
%e A255555   14, 26, 50,  98, 194, 386,  770, 1538, 3074, 6146, 12290, 24578
%e A255555   17, 34, 67, 134, 266, 530, 1058, 2114, 4226, 8450, 16898, 33794
%e A255555   20, 39, 78, 153, 304, 606, 1207, 2411, 4818, 9631, 19259, 38512
%e A255555   ...
%o A255555 (Scheme)
%o A255555 (define (A255555 n) (A255555bi (A002260 n) (A004736 n)))
%o A255555 (define (A255555bi row col) (if (= 1 col) (if (= 1 row) 1 (A055938 (- row 1))) (A005187 (+ 1 (A255555bi row (- col 1))))))
%Y A255555 Inverse permutation: A255556.
%Y A255555 Transpose: A255557.
%Y A255555 Row 1: A000225.
%Y A255555 Cf. A005187, A055938.
%Y A255555 Cf. A255559 (column index), A255560 (row index).
%Y A255555 Cf. also A254105, A256995 (variants), A233275-A233278.
%K A255555 nonn,tabl
%O A255555 1,2
%A A255555 _Antti Karttunen_, Apr 13 2015