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A126940 "Model 2" for number of free alkanes on n points. 4
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; text; internal format)
OFFSET

0,3

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).

LINKS

Table of n, a(n) for n=0..27.

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].

Empirical g.f.: (x^5+x^4+3*x^3+x-1) / (x^6+4*x^5+4*x^4+7*x^3+x^2+2*x-1). - Colin Barker, Apr 08 2013

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:

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

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 18 2007

STATUS

approved

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Last modified September 22 03:52 EDT 2020. Contains 337289 sequences. (Running on oeis4.)