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A126940
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"Model 2" for number of free alkanes on n points.
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4
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1, 1, 3, 11, 35, 109, 347, 1105, 3507, 11135, 35371, 112343, 356797, 1133207, 3599143, 11431063, 36305649, 115308721, 366226729, 1163155753, 3694245273, 11733121945, 37265026883, 118355731271, 375904173873, 1193891891823, 3791864917001, 12043167097497
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| 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
| 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
| 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-2]+c[n-4];
c[n]:=2*a[n-1]+b[n-1]+b[n-2]+b[n-3]+c[n-3]+c[n-4];
d[n]:=b[n-1]+b[n-2]+c[n-1]+c[n-2]+c[n-3]; od:
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CROSSREFS
| For sequences b[n], c[n], d[n] and a[n]+b[n]+c[n]+d[n] see A126946, A126947, A126948, A126945 respectively.
Sequence in context: A027060 A171498 A126939 * A026125 A026154 A025181
Adjacent sequences: A126937 A126938 A126939 * A126941 A126942 A126943
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 18 2007
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