A277199 Square array A(n,k) = A048720(n, A065621(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, 7, 4, 3, 4, 14, 6, 4, 13, 8, 9, 8, 5, 14, 26, 12, 28, 10, 6, 11, 28, 23, 16, 27, 12, 7, 8, 22, 18, 52, 20, 18, 14, 8, 25, 16, 29, 56, 57, 24, 21, 16, 9, 26, 50, 24, 44, 54, 46, 28, 56, 18, 10, 31, 52, 43, 32, 39, 36, 35, 32, 63, 20, 11, 28, 62, 46, 100, 40, 58, 42, 104, 36, 54, 22, 12, 21, 56, 33, 104, 125, 48, 49, 112, 101, 40, 49, 24, 13

Offset

1,2

Comments

See A277320.

Links

Antti Karttunen, Table of n, a(n) for n = 1..7260; the first 120 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(n, k) = A048720(n, A065621(k)) = A277320(k, n).

Example

The top left corner of the array:
n\k  |  1   2   3   4    5    6    7    8    9   10   11   12   13   14   15
-----+-----------------------------------------------------------------------
  1  |  1,  2,  7,  4,  13,  14,  11,   8,  25,  26,  31,  28,  21,  22,  19,
  2  |  2,  4, 14,  8,  26,  28,  22,  16,  50,  52,  62,  56,  42,  44,  38,
  3  |  3,  6,  9, 12,  23,  18,  29,  24,  43,  46,  33,  36,  63,  58,  53,
  4  |  4,  8, 28, 16,  52,  56,  44,  32, 100, 104, 124, 112,  84,  88,  76,
  5  |  5, 10, 27, 20,  57,  54,  39,  40, 125, 114,  99, 108,  65,  78,  95,
  6  |  6, 12, 18, 24,  46,  36,  58,  48,  86,  92,  66,  72, 126, 116, 106,
  7  |  7, 14, 21, 28,  35,  42,  49,  56,  79,  70,  93,  84, 107,  98, 121,
  8  |  8, 16, 56, 32, 104, 112,  88,  64, 200, 208, 248, 224, 168, 176, 152,
  9  |  9, 18, 63, 36, 101, 126,  83,  72, 209, 202, 231, 252, 189, 166, 139,
 10  | 10, 20, 54, 40, 114, 108,  78,  80, 250, 228, 198, 216, 130, 156, 190,
 11  | 11, 22, 49, 44, 127,  98,  69,  88, 227, 254, 217, 196, 151, 138, 173,
 12  | 12, 24, 36, 48,  92,  72, 116,  96, 172, 184, 132, 144, 252, 232, 212,
 13  | 13, 26, 35, 52,  81,  70, 127, 104, 181, 162, 155, 140, 233, 254, 199,
 14  | 14, 28, 42, 56,  70,  84,  98, 112, 158, 140, 186, 168, 214, 196, 242,
 15  | 15, 30, 45, 60,  75,  90, 105, 120, 135, 150, 165, 180, 195, 210, 225,

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);
A277199_sq(x, y) = A048720(x, A065621(y));
A277199list(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] = A277199_sq(col, (a-(col-1))))); (v); };
v277199 = A277199list(up_to);
A277199(n) = v277199[n]; \\ Antti Karttunen, Dec 06 2025
(Scheme) (define (A277199 n) (A277320bi (A004736 n) (A002260 n))) ;; Code for A277320bi given in A277320.

Crossrefs

Transpose of square array A277320.

Cf. A391244 (lower triangle).

Main diagonal: A277699.

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

Column 1: A000027, Column 3: A048727.

Cf. A048720.

Sequence in context: A115025 A245286 A075428 * A116077 A074144 A239383

Adjacent sequences: A277196 A277197 A277198 * A277200 A277201 A277202

Keyword

nonn,base,tabl

Author

Antti Karttunen, Nov 01 2016

Status

approved