A126940 "Model 2" for number of free alkanes on n points.

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

Offset

0,3

Comments

Linear recurrence and empirical g.f confirmed for more terms. - Ray Chandler, Mar 07 2024

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

Ray Chandler, Table of n, a(n) for n = 0..1993

Index entries for linear recurrences with constant coefficients, signature (2, 1, 7, 4, 4, 1).

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: A171498 A126939 A370199 * A026125 A026154 A025181

Adjacent sequences: A126937 A126938 A126939 * A126941 A126942 A126943

Keyword

nonn

Author

N. J. A. Sloane, Mar 18 2007

Status

approved