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- W4253228384 abstract "The Lucas sequence is defined by:<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=[ L_0 = 2,L_1 = 1,L_n = L_{n - 1} + L_{n - 2} ]><mml:msub><mml:mi>L</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>for<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=[ n geqslant 2 ]><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math>. Let<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$V(n)$><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$r(n)$><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>denote respectively the number of partitions of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$n$><mml:mi>n</mml:mi></mml:math>into parts, distinct parts from<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${L_n}$><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math>. We develop formulas that facilitate the computation of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$V(n)$><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$r(n)$><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>." @default.
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- W4253228384 date "1998-01-01" @default.
- W4253228384 modified "2023-09-24" @default.
- W4253228384 title "Lucas partitions" @default.
- W4253228384 doi "https://doi.org/10.1155/s0161171298000532" @default.
- W4253228384 hasPublicationYear "1998" @default.
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