A391244 Triangular table T(n,k) = A048720(n, A065621(k)), n >= 1, 1 <= k <= n, read by rows.

1, 2, 4, 3, 6, 9, 4, 8, 28, 16, 5, 10, 27, 20, 57, 6, 12, 18, 24, 46, 36, 7, 14, 21, 28, 35, 42, 49, 8, 16, 56, 32, 104, 112, 88, 64, 9, 18, 63, 36, 101, 126, 83, 72, 209, 10, 20, 54, 40, 114, 108, 78, 80, 250, 228, 11, 22, 49, 44, 127, 98, 69, 88, 227, 254, 217, 12, 24, 36, 48, 92, 72, 116, 96, 172, 184, 132, 144

Offset

1,2

Links

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

Index entries for sequences related to binary expansion of n.

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

Formula

T(n, k) = A277199(n, k), for n >= 1, and 1 <= k <= n.

Example

Triangle T(n, k) = A277199(n, k) is read as T(1,1), T(2,1), T(2,2), T(3,1), T(3,2), T(3,3), etc, and begins as:
   1;
   2,   4;
   3,   6,   9;
   4,   8,  28,  16;
   5,  10,  27,  20,  57;
   6,  12,  18,  24,  46,  36;
   7,  14,  21,  28,  35,  42,  49;
   8,  16,  56,  32, 104, 112,  88,  64;
   9,  18,  63,  36, 101, 126,  83,  72, 209;
  10,  20,  54,  40, 114, 108,  78,  80, 250, 228;
  11,  22,  49,  44, 127,  98,  69,  88, 227, 254, 217;
  12,  24,  36,  48,  92,  72, 116,  96, 172, 184, 132, 144;
  etc.

Prog

(PARI)
up_to = 78;
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));
A391244list(up_to) = { my(v = vector(up_to), i=0); for(n=1, oo, for(k=1, n, if(i++ > up_to, return(v)); v[i] = A277199_sq(n, k))); (v); };
v391244 = A391244list(up_to);
A391244(n) = v391244[n]; \\ Antti Karttunen, Dec 06 2025

Crossrefs

Lower triangle of square array A277199, each row up to and including its main diagonal.

Cf. also triangles A075362, A391245 and sequence A391246.

Cf. A000027 (left edge), A277699 (right edge).

Sequence in context: A075362 A377133 A110749 * A077529 A143516 A120620

Adjacent sequences: A391241 A391242 A391243 * A391245 A391246 A391247

Keyword

nonn,tabl

Author

Antti Karttunen, Dec 06 2025

Status

approved