A141290 Triangle read by rows, descending antidiagonals of a (1, 3, 5, ...) * (1, 4, 16, ...) multiplication table.

1, 3, 4, 5, 12, 16, 7, 20, 48, 64, 9, 28, 80, 192, 256, 11, 36, 112, 320, 768, 1024, 13, 44, 144, 448, 1280, 3072, 4096, 15, 52, 176, 576, 1792, 5120, 12288, 16384, 17, 60, 208, 704, 2304, 7168, 20480, 49152, 65536, 19, 68, 240, 832, 2816, 9216, 28672, 81920, 196608, 262144

Offset

1,2

Comments

Binary representation of all terms ends in an even number of zeros (cf. A003159).

Links

Table of n, a(n) for n=1..55.

Formula

From Stefano Spezia, May 21 2024: (Start)

G.f. as array: x*y*(1 + y)/((1 - 4*x)*(1 - y)^2).

E.g.f. as array: (exp(4*x) - 1)*(exp(y)*(1 - 2*y) - 1)/4. (End)

Example

Given the multiplication table (1, 3, 5, ...) * (1, 4, 16, ...); i.e., odd numbers as column headings, powers of 4 along the left border:
   1,   3,   5,   7, ...
   4,  12,  20,  28, ...
  16,  48,  80, 112, ...
  64, 192, 320, 448, ...
  ...
Rows of the triangle = descending antidiagonals of the array, getting:
   1;
   3,  4;
   5, 12,  16;
   7, 20,  48,  64;
   9, 28,  80, 192,  256;
  11, 36, 112, 320,  768, 1024;
  13, 44, 144, 448, 1280, 3072,  4096;
  15, 52, 176, 576, 1792, 5120, 122288, 16384;
  ...

Mathematica

A[n_, k_]:=(2k-1)*4^(n-1); Table[A[k, n-k+1], {n, 10}, {k, n}]//Flatten (* Stefano Spezia, May 21 2024 *)

Crossrefs

Cf. A003159, A141291.

Sequence in context: A090829 A374221 A236244 * A010752 A049929 A262192

Adjacent sequences: A141287 A141288 A141289 * A141291 A141292 A141293

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 22 2008

Extensions

a(14), a(36) corrected by Peter Munn, Aug 27 2019

Status

approved