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

Author

Gary W. Adamson, Jun 22 2008

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
  ...
		

Crossrefs

Cf. A003159, A141291.

Programs

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 *)

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)

Extensions

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