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A141290
Triangle read by rows, descending antidiagonals of a (1, 3, 5, ...) * (1, 4, 16, ...) multiplication table.
3
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).
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
Sequence in context: A090829 A374221 A236244 * A010752 A049929 A262192
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 22 2008
EXTENSIONS
a(14), a(36) corrected by Peter Munn, Aug 27 2019
STATUS
approved