Online encyclopedia of Number Pyramids
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Pyramid 1
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$$U_{1}(x, y) = x + y$$
Pyramid 2
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$$U_{2}(x, y) = x \left(y + 1\right)$$
Pyramid 3
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$$U_{3}(x, y) = y \left(x + 1\right)$$
Pyramid 4
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$$U_{4}(x, y) = x y + x + y$$
Pyramid 5
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$$U_{5}(x, y) = x + \frac{y}{1 - x}$$
Pyramid 6
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$$U_{6}(x, y) = \frac{x}{1 - y} + y$$
Pyramid 7
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$$U_{7}(x, y) = \left(x + 1\right) \left(x + y\right)$$
Pyramid 8
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$$U_{8}(x, y) = \left(x + y\right) \left(y + 1\right)$$
Pyramid 9
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$$U_{9}(x, y) = x^{2} + x + y$$
Pyramid 10
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$$U_{10}(x, y) = \left(x + 1\right) \left(y + 1\right)$$
Pyramid 11
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$$U_{11}(x, y) = \frac{x + 1}{- y \left(x + 1\right) + 1}$$
Pyramid 12
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$$U_{12}(x, y) = \frac{y + 1}{- x y - x + 1}$$
Pyramid 13
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$$U_{13}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{2} - 8 x - 4\right) + 1}}{y \left(2 x + 2\right)}$$
Pyramid 14
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$$U_{14}(x, y) = \frac{- x - y - \sqrt{x^{2} - 2 x + y^{2} + y \left(- 2 x - 2\right) + 1} + 1}{2 x y}$$
Pyramid 15
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$$U_{15}(x, y) = \frac{1}{\left(x + 1\right) \left(y + 1\right)}$$
Pyramid 16
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$$U_{16}(x, y) = \frac{1 - \sqrt{- 4 x y^{2} - 8 x y - 4 x + 1}}{2 x \left(y + 1\right)}$$
Pyramid 17
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$$U_{17}(x, y) = \frac{x + 1}{1 - y}$$
Pyramid 18
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$$U_{18}(x, y) = \frac{1 - \sqrt{y \left(- 4 x - 4\right) + 1}}{2 y}$$
Pyramid 19
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$$U_{19}(x, y) = - \frac{1}{x + y - 1}$$
Pyramid 20
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$$U_{20}(x, y) = \frac{1 - \sqrt{- 4 x - 4 y + 1}}{2 x + 2 y}$$
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