|
%I #21 Nov 05 2016 07:23:01
%S 1,3,2,5,6,7,15,10,9,4,17,30,27,12,13,51,34,45,20,23,14,85,102,119,60,
%T 57,18,11,255,170,153,68,75,54,29,8,257,510,427,204,221,90,39,24,25,
%U 771,514,765,340,359,238,105,40,43,26,1285,1542,1799,1020,937,306,187,120,125,46,31,3855,2570,2313,1028,1275,854,461,136,135,114,33,28
%N Square array: A(r,1) = A065621(r); for c > 1, A(r,c) = A048724(A(r,c-1)), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
%C For all n >= 1, A277818 (= A268389(n)+1) gives the (one-based) index of the column where n is located in this array, while A268671(n) gives the (one-based) index of the row where it is on.
%C This array is obtained when one selects from A277320 the columns 1, 3, 5, 15, 17, 51, ..., i.e., those with an index A001317(k).
%H Antti Karttunen, <a href="/A277820/b277820.txt">Table of n, a(n) for n = 1..3321; the first 81 antidiagonals of the array</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A(r,1) = A065621(r); for c > 1, A(r,c) = A048724(A(r,c-1)).
%F A(r,c) = A048675(A277810(r,c)).
%F As a composition of other permutations:
%F a(n) = A277901(A277880(n)).
%e The top left corner of the array:
%e 1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855
%e 2, 6, 10, 30, 34, 102, 170, 510, 514, 1542, 2570, 7710
%e 7, 9, 27, 45, 119, 153, 427, 765, 1799, 2313, 6939, 11565
%e 4, 12, 20, 60, 68, 204, 340, 1020, 1028, 3084, 5140, 15420
%e 13, 23, 57, 75, 221, 359, 937, 1275, 3341, 5911, 14649, 19275
%e 14, 18, 54, 90, 238, 306, 854, 1530, 3598, 4626, 13878, 23130
%e 11, 29, 39, 105, 187, 461, 599, 1785, 2827, 7453, 10023, 26985
%e 8, 24, 40, 120, 136, 408, 680, 2040, 2056, 6168, 10280, 30840
%e 25, 43, 125, 135, 393, 667, 1965, 2295, 6425, 11051, 32125, 34695
%e 26, 46, 114, 150, 442, 718, 1874, 2550, 6682, 11822, 29298, 38550
%e 31, 33, 99, 165, 495, 561, 1619, 2805, 7967, 8481, 25443, 42405
%e 28, 36, 108, 180, 476, 612, 1708, 3060, 7196, 9252, 27756, 46260
%e 21, 63, 65, 195, 325, 975, 1105, 3315, 5397, 16191, 16705, 50115
%e 22, 58, 78, 210, 374, 922, 1198, 3570, 5654, 14906, 20046, 53970
%e 19, 53, 95, 225, 291, 869, 1455, 3825, 4883, 13621, 24415, 57825
%e 16, 48, 80, 240, 272, 816, 1360, 4080, 4112, 12336, 20560, 61680
%e 49, 83, 245, 287, 801, 1379, 4005, 4335, 12593, 21331, 62965, 73247
%e 50, 86, 250, 270, 786, 1334, 3930, 4590, 12850, 22102, 64250, 69390
%e 55, 89, 235, 317, 839, 1481, 3675, 4845, 14135, 22873, 60395, 80957
%o (Scheme)
%o (define (A277820 n) (A277820bi (A002260 n) (A004736 n)))
%o (define (A277820bi row col) (if (= 1 col) (A065621 row) (A048724 (A277820bi row (- col 1)))))
%Y Inverse permutation: A277821.
%Y Transpose: A277819.
%Y Cf. A048724, A065621.
%Y Row 1: A001317.
%Y Column 1: A065621, column 2: A277823, column 3: A277825.
%Y Cf. A268389, A277818, A268671.
%Y Cf. also A193231, A277320, A277810, A276618 (A099884), A248513.
%Y Other related tables or permutations: A277880, A277901.
%K nonn,tabl,base
%O 1,2
%A _Antti Karttunen_, Nov 01 2016
|
