Revision History for A141525
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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| A141525
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a(n) = a(n-2) + a(n-3) if n == 0 (mod 3), a(n-1) + a(n-4) if n == 0 (mod 4), otherwise a(n-2) with a(0) = 0 and a(1) = a(2) = a(3) = 1.
(history;
published version)
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#12 by Joerg Arndt at Tue Mar 30 05:21:00 EDT 2021
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#11 by Michel Marcus at Tue Mar 30 01:50:01 EDT 2021
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#10 by Joerg Arndt at Tue Mar 30 00:11:31 EDT 2021
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#9 by Joerg Arndt at Tue Mar 30 00:11:26 EDT 2021
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| NAME
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a(n) = a(n-2) + a(n-3) if n == 0 (mod 3 = 0, ), a(n-1) + a(n-4) if n == 0 (mod 4 = 0, ), otherwise a(n-2) with a(0) = 0 and a(1) = a(2) = a(3) = 1.
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| FORMULA
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a(n) = a(n-2) + a(n-3) if n mod 3 = 0, a(n-1) + a(n-4) if n mod 4 = 0, otherwise a(n-2) with a(0) = 0 and a(1) = a(2) = a(3) = 1.
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proposed
editing
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#8 by Jon E. Schoenfield at Mon Mar 29 23:48:45 EDT 2021
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#7 by Jon E. Schoenfield at Mon Mar 29 23:48:43 EDT 2021
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| FORMULA
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a(n) = a(n-2) + a(n-3) if n mod(n, 3) = = 0, a(n-1) + a(n-4) if n mod(n, 4) = = 0, otherwise a(n-2) with a(0) = 0 and a(1) = a(2) = a(3) = 1.
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proposed
editing
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#6 by Jon E. Schoenfield at Mon Mar 29 23:29:11 EDT 2021
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#5 by Jon E. Schoenfield at Mon Mar 29 23:29:09 EDT 2021
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| NAME
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a(n) = a(n-2) + a(n-3) if n mod(n, 3) = = 0, a(n-1) + a(n-4) if n mod(n, 4) = = 0, otherwise a(n-2) with a(0) = 0 and a(1) = a(2) = a(3) = 1.
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| COMMENTS
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LimitLim_{n -> infinity} <a(n+1)/a(n)> = 1.324717957244746, where <> is the expectation value.
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proposed
editing
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#4 by G. C. Greubel at Mon Mar 29 21:24:13 EDT 2021
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#3 by G. C. Greubel at Mon Mar 29 21:22:57 EDT 2021
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| NAME
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A low average ratio switched sequence: a(n)=If[Mod[n, 3] == 0, ) = a(n - -2) + a(n - -3), If) if mod(Mod[n, 4) == 3) = 0, a(n - -1) + a(n-4) if mod(n - , 4), ) = 0, otherwise a(n - -2) with a(0) = 0 and a(1), ) = a(n - 2)]].) = a(3) = 1.
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| DATA
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0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 8, 8, 8, 16, 24, 24, 40, 40, 64, 80, 80, 80, 160, 160, 160, 320, 480, 480, 800, 800, 1280, 1600, 1600, 1600, 3200, 3200, 3200, 6400, 9600, 9600, 16000, 16000, 25600, 32000, 32000, 32000, 64000, 64000, 64000, 128000, 192000, 192000, 320000, 320000, 512000, 640000, 640000, 640000, 1280000
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| OFFSET
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10,7
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| COMMENTS
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While appearing to be an "even" output or maybe a "regular" sequence the average ratio limit( using <> as expectation value):
Limit[<_{n -> infinity} <a(n+1)/a(n)>,n->Infinity]=)> = 1.324717957244746;, where <> is the expectation value.
real root of x^3-x-1 ( Padovan/ minimal Pisot root).
I got this by accident I meant to type in:
a[n] = If[Mod[n, 3] == 0, a[n - 2] + a[n - 3], If[Mod[n, 4] == 0, a[n - 1] + a[n - 4], a[n - 1] + a[n - 2]]];
which gives a different result!
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| LINKS
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G. C. Greubel, <a href="/A141525/b141525.txt">Table of n, a(n) for n = 0..500</a>
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| FORMULA
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a(n)=If[Mod[n, 3] == 0, ) = a(n - -2) + a(n - -3), If) if mod(Mod[n, 4) == 3) = 0, a(n - -1) + a(n-4) if mod(n - , 4), ) = 0, otherwise a(n - -2) with a(0) = 0 and a(1), ) = a(n - 2)]].) = a(3) = 1.
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| MATHEMATICA
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Clear[a] a[0] = 0; a[1] = 1; a[2] = 1; n_]:= a[3] = 1; an]= If[n_] := a==0, 0, If[n] = <4, 1, If[Mod[n, 3] == ]==0, a[n - -2] + a[n - -3], If[Mod[n, , 4] == ] ==0, a[n - -1] + a[n - -4], a[n - -1], a[n - 2]]]; Table[a[n], {n, 0, 40}]] ]]]];
Table[a[n], {n, 0, 65}] (* modified by G. C. Greubel, Mar 29 2021 *)
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| PROG
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(Magma)
function a(n)
if n eq 0 then return 0;
elif n lt 4 then return 1;
elif (n mod 3) eq 0 then return a(n-2) + a(n-3);
elif (n mod 4) eq 0 then return a(n-1) + a(n-4);
else return a(n-1);
end if; return a;
end function;
[a(n): n in [0..65]]; // G. C. Greubel, Mar 29 2021
(Sage)
@CachedFunction
def a(n):
if (n==0): return 0
elif (n<4): return 1
elif (n%3==0): return a(n-2) + a(n-3)
elif (n%4==0): return a(n-1) + a(n-4)
else: return a(n-1)
[a(n) for n in (0..65)] # G. C. Greubel, Mar 29 2021
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| KEYWORD
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nonn,uned,tabl
nonn
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| EXTENSIONS
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Edited by G. C. Greubel, Mar 29 2021
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| STATUS
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approved
editing
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