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A141290
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Triangle read by rows, descending antidiagonals of a (1, 3, 5, ...) * (1, 4, 16, ...) multiplication table.
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3
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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
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history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Binary representation of all terms ends in an even number of zeros (cf. A003159).
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LINKS
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FORMULA
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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)
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EXAMPLE
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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;
...
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MATHEMATICA
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A[n_, k_]:=(2k-1)*4^(n-1); Table[A[k, n-k+1], {n, 10}, {k, n}]//Flatten (* Stefano Spezia, May 21 2024 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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