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1, 4, 9, 1, 16, 4, 25, 9, 1, 36, 16, 4, 49, 25, 9, 1, 64, 36, 16, 4, 81, 49, 25, 9, 1, 100, 64, 36, 16, 4, 121, 81, 49, 25, 9, 1, 144, 100, 64, 36, 16, 4, 169, 121, 81, 49, 25, 9, 1
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OFFSET
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1,2
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COMMENTS
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Row sums = A000292, the tetrahedral numbers.
Let the triangle = M. Then lim_{n->inf} M^n = A173277 as a left-shifted vector: (1, 4, 13, 32, 74, 152, 298, ...) = A(x), where A(x) satisfies A000290 = A(x)/A(x^2), A000290 = integer squares.
M * [1, 2, 3, ...] = A001752: (1, 4, 11, 24, 46, 80, 130, ...).
M * [1, 3, 6, 10, ...] = A028346: (1, 4, 12, 28, 58, 108, ...). (End)
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LINKS
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FORMULA
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EXAMPLE
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First few rows of the triangle:
1;
4;
9, 1;
16, 4;
25, 9, 1;
36, 16, 4;
49, 25, 9, 1;
64, 36, 16, 4;
81, 49, 25, 9, 1;
100, 64, 36, 16, 4;
121, 81, 49, 25, 9, 1;
144, 100, 64, 36, 16, 4;
169, 121, 81, 49, 25, 9, 1;
...
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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