A277320 Square array A(n,k) = A048720(A065621(n), k), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

1, 2, 2, 3, 4, 7, 4, 6, 14, 4, 5, 8, 9, 8, 13, 6, 10, 28, 12, 26, 14, 7, 12, 27, 16, 23, 28, 11, 8, 14, 18, 20, 52, 18, 22, 8, 9, 16, 21, 24, 57, 56, 29, 16, 25, 10, 18, 56, 28, 46, 54, 44, 24, 50, 26, 11, 20, 63, 32, 35, 36, 39, 32, 43, 52, 31, 12, 22, 54, 36, 104, 42, 58, 40, 100, 46, 62, 28, 13, 24, 49, 40, 101, 112, 49, 48, 125, 104, 33, 56, 21

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array

Index entries for sequences related to binary expansion of n

Index entries for sequences operating on polynomials in ring GF(2)[X]

Formula

A(r,c) = A048720(A065621(r), c).

Example

The top left corner of the array:
n\k |  1    2    3    4    5    6    7    8    9   10   11   12
----+------------------------------------------------------------
  1 |  1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12
  2 |  2,   4,   6,   8,  10,  12,  14,  16,  18,  20,  22,  24
  3 |  7,  14,   9,  28,  27,  18,  21,  56,  63,  54,  49,  36
  4 |  4,   8,  12,  16,  20,  24,  28,  32,  36,  40,  44,  48
  5 | 13,  26,  23,  52,  57,  46,  35, 104, 101, 114, 127,  92
  6 | 14,  28,  18,  56,  54,  36,  42, 112, 126, 108,  98,  72
  7 | 11,  22,  29,  44,  39,  58,  49,  88,  83,  78,  69, 116
  8 |  8,  16,  24,  32,  40,  48,  56,  64,  72,  80,  88,  96
  9 | 25,  50,  43, 100, 125,  86,  79, 200, 209, 250, 227, 172
 10 | 26,  52,  46, 104, 114,  92,  70, 208, 202, 228, 254, 184
 11 | 31,  62,  33, 124,  99,  66,  93, 248, 231, 198, 217, 132
 12 | 28,  56,  36, 112, 108,  72,  84, 224, 252, 216, 196, 144
 13 | 21,  42,  63,  84,  65, 126, 107, 168, 189, 130, 151, 252
 14 | 22,  44,  58,  88,  78, 116,  98, 176, 166, 156, 138, 232
 15 | 19,  38,  53,  76,  95, 106, 121, 152, 139, 190, 173, 212
 16 | 16,  32,  48,  64,  80,  96, 112, 128, 144, 160, 176, 192
 17 | 49,  98,  83, 196, 245, 166, 151, 392, 441, 490, 475, 332
 18 | 50, 100,  86, 200, 250, 172, 158, 400, 418, 500, 454, 344
 19 | 55, 110,  89, 220, 235, 178, 133, 440, 399, 470, 481, 356

Prog

(PARI)
up_to = 10440;
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
A277320_sq(x, y) = A048720(A065621(x), y);
A277320list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A277320_sq(col, (a-(col-1))))); (v); };
v277320 = A277320list(up_to);
A277320(n) = v277320[n]; \\ Antti Karttunen, Dec 06 2025
(Scheme)
(define (A277320 n) (A277320bi (A002260 n) (A004736 n)))
(define (A277320bi row col) (A048720bi (A065621 row) col))

Crossrefs

Transpose: A277199.

Main diagonal: A277699.

Row 1: A000027, Row 3: A048727.

Column 1: A065621, Column 3: A277823, Column 5: A277825.

Cf. A277820 (array obtained by selecting only the columns with an index A001317(k), k=0..), A379221 (another subarray).

Cf. A048720, A115872.

Sequence in context: A319638 A179637 A054241 * A343399 A332106 A088633

Adjacent sequences: A277317 A277318 A277319 * A277321 A277322 A277323

Keyword

nonn,base,tabl

Author

Antti Karttunen, Nov 01 2016

Status

approved