View source for Sequence Lily

<templatestyles src="Template:Boolf-seq-legend/style.css" />
{{DISPLAYTITLE:Sequence ''Lily''}}
{{Boolf sequences header}}
{{Boolf sequences header/Willow and Poplar}}

==Sequence ''Lily<sub>(Drop)</sub>''==

{| class="wikitable" style="text-align: center;"
|+ 
!
! 0 !!  1  !!  2  !!  3  !!  4  !!  5  !!  6 !!  7
|-
! 🌊 ''Lily''
| 2 || 2 || 8 || 184 || 62464 || 4293001088 || 18446743803209556992 || 340282366920938461120638132973980614656
|- 
! 💧 ''LilyDrop''
| 2 ||style="color: gray;"| 0 || 6 || 176 || 62280 || 4292938624 || 18446743798916555904 || 340282366920938461102191389170771057664
|}

{| class="boolf-seq-legend"
|class="nutshell"| ''a'' ↦ strong
|colspan="4" class="left right"| Lily(''a'') is the number of {{boolf-prop|strong}} <abbr title="Boolean functions">BF</abbr> with {{boolf-prop|arity}} ''a''.
|-
|class="nutshell"| ''a'' ↦ depth 0
|class="wrapper"|
<!--START NESTED TABLE-->
{| class="boolf-seq-legend-nested"
| Lily(''a'')<br><span class="drop">LilyDrop(''a'')</span>
| is the number of <abbr title="Boolean functions">BF</abbr> with
|{{boolf-prop|arity}}<br><span class="drop">{{boolf-prop|adicity}}</span>
| ''a'' and {{boolf-prop|soft depth}} 0.
|}
<!--END NESTED TABLE-->
|}

{{Collapsible START|''Lily'' is the product of {{Boolf-seq|Aloe}} and the powers of two.|collapsed wide}}
<math>\text{Lily}(n) = {\color{Green}\text{Aloe}(n)} \cdot {\color{Red}2^n}</math>
{{Sequence pair Lily/wave}}
{{Collapsible END}}

=={{anchor|small}}Sequence ''SmallLily<sub>(Drop)</sub>''==

''SmallLily'' differs from ''Lily'' only in the first entry.<br>
''SmallLily<sub>(Drop)</sub>'' are the left columns of {{Boolf-seq|SmallTurnedPoplar|''SmallTurnedPoplar<sub>(Drop)</sub>''}}.

{| class="wikitable" style="text-align: center;"
|+ 
!
! 0 !!  1  !!  2  !!  3  !!  4
|-
! 🌊 ''SmallLily'' <small>({{oeis|A305737}})</small>
| 1 || 2 || 8 || 184 || 62464
|- 
! 💧 ''SmallLilyDrop''
| 1 || 1 || 6 || 176 || 62280
|}

{| class="boolf-seq-legend"
|class="nutshell"| ''a'' ↦ depth 0
|class="left"| SmallLily(''a'')<br><span class="drop">SmallLilyDrop(''a'')</span>
| is the number of <abbr title="Boolean functions">BF</abbr> with
| {{boolf-prop|arity}}<br><span class="drop">{{boolf-prop|adicity}}</span>
|class="right"| ''a'' and {{boolf-prop|depth}} 0.
|}

{{Collapsible START| row sums of ''SignedCypress'' |open wide}}
{{Triangle SignedCypress}}
{{Collapsible END}}



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