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Search: id:A126939
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| A126939 |
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"Model 1" for number of free alkanes on n points. |
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+0
5
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| 1, 1, 3, 11, 35, 107, 339, 1073, 3375, 10633, 33525, 105651, 332941, 1049305, 3306957, 10421967, 32845327, 103513709, 326228241, 1028123557, 3240180157, 10211580633, 32182277499, 101423965833, 319642412979, 1007368140211, 3174768208785, 10005431759263
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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Gy. Tasi et al., Quantum algebraic-combinatoric study of the conformational properties of n-alkanes II, J. Math. Chemistry, 27 (2000), 191-199 (see Table 1).
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FORMULA
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Define sequences a[n], b[n], c[n], d[n] by the recurrences shown in the Maple code below. Sequence gives values of a[n], and also (with a different offset) a[n]+b[n]+d[n].
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MAPLE
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M:=35; a:=array(-5..M); b:=array(-5..M); c:=array(-5..M); d:=array(-5..M);
for i from -5 to 0 do a[i]:=0; b[i]:=0; c[i]:=0; d[i]:=0; od: a[0]:=1;
for n from 1 to M do
a[n]:=a[n-1]+b[n-1]+d[n-1];
b[n]:=2*a[n-1]+b[n-1]+b[n-3]+c[n-3]+c[n-4];
c[n]:=2*a[n-1]+b[n-1]+b[n-2]+b[n-3]+2*c[n-3]+c[n-4];
d[n]:=b[n-1]+b[n-2]+c[n-1]+2*c[n-2]+c[n-3]; od:
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CROSSREFS
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For sequences b[n], c[n], d[n] and a[n]+b[n]+c[n]+d[n] see A126941, A126942, A126943, A126944 respectively.
Adjacent sequences: A126936 A126937 A126938 this_sequence A126940 A126941 A126942
Sequence in context: A057838 A088578 A027060 this_sequence A126940 A026125 A026154
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KEYWORD
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nonn
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AUTHOR
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njas, Mar 18 2007
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