I need help solving these recurrence relations | Mathematics | Page 1

light spindle Oct 9, 2024, 9:34 PM

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g1(n) is just n!, g2(1)=0, g3(1)=0

dawn zealotBOT Oct 9, 2024, 9:34 PM

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light spindle Oct 9, 2024, 9:36 PM

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$g_1{(n)}=n!$, $g_2{(1)}=0$, $g_3{(1)}=0$

sudden spindleBOT Oct 9, 2024, 9:36 PM

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MrMasterGamer0

light spindle Oct 9, 2024, 9:42 PM

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Some more context:

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I have this “triangle” (more of a parallelogram as the 0s extend left of the 1) where terms to the left and right are added together then multiplied by the smaller number between. The recurrence relations represent the equations of diagonal.

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A closed form for g_2 and g_3 would be awesome, and a closed form of g_k would be even better. But I at least need help figuring out how to do all that.

light spindle Oct 10, 2024, 12:06 AM

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@dawn zealot

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<@&286206848099549185>

light spindle Oct 10, 2024, 1:48 AM

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$g_1{(n)}=(g_1{(n-1)}+0)n=n!$;
$g_2{(n)}=(g_2{(n-1)}+g_1{(n-1)})(n-2)$, $g_2{(1)}=0$;
$g_3{(n)}=(g_3{(n-1)}+g_2{(n-1)})(n-4)$, $g_3{(1)}=0$

sudden spindleBOT Oct 10, 2024, 1:48 AM

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MrMasterGamer0

light spindle Oct 10, 2024, 2:10 AM

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.solved

dawn zealotBOT Oct 10, 2024, 2:10 AM

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Solved

Post marked as solved by @light spindle.

Use .unsolved if this was a mistake.

light spindle Oct 12, 2024, 7:40 AM

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.unsolved

#I need help solving these recurrence relations