A036996 Number of isomers of alkyl homologs of adamantane with n carbon atoms.

1, 2, 11, 49, 217, 858, 3314, 11995, 41921, 141163, 462674, 1480017, 4644331, 14332801, 43628996, 131248423, 390921934, 1154427742, 3384244322, 9858374939, 28560865688, 82351168539, 236465407302, 676536049902, 1929455222816

Offset

0,2

References

M. Yu. Kornilov, Number of structural isomers in the adamantane series, J. Structural Chem. 16 (3) (1975), 466-468.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..700

Formula

Reference gives a g.f.

Maple

A:= proc(n) option remember; unapply(`if`(n=0, 1, convert(series(1+ x/6 *(A(n-1)(x)^3 +3*A(n-1)(x) *A(n-1)(x^2) +2*A(n-1)(x^3)), x, n+1), polynom)), x) end: f:= (n, m)-> A(n)(x^m): gf:= n-> (f(n, 1)^16 +3*f(n, 2)^8 +8*f(n, 1) *f(n, 3)^5 +6*f(n, 1)^4 *f(n, 2)^6 +6*f(n, 4)^4)/24: a:= n-> coeff(gf(n), x, n): seq(a(n), n=0..35); # Alois P. Heinz, Jul 29 2009

Mathematica

A[0] = 1&; A[n_][x_] := A[n][x] = Normal[Series[1+y/6*(A[n-1][y]^3+3*A[n-1][y]*A[n-1][y^2]+2*A[n-1][y^3]), {y, 0, n+1}]] /. y -> x; f[n_, m_] := A[n][x^m]; gf[n_] := (f[n, 1]^16+3*f[n, 2]^8+8*f[n, 1]*f[n, 3]^5+6*f[n, 1]^4*f[n, 2]^6+6*f[n, 4]^4)/24; a[n_] := Coefficient[gf[n], x, n]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Feb 13 2014, after Alois P. Heinz's Maple code *)

Crossrefs

Cf. A000598. - Alois P. Heinz, Jul 29 2009

Sequence in context: A139475 A034568 A265610 * A262296 A151314 A316263

Adjacent sequences: A036993 A036994 A036995 * A036997 A036998 A036999

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Alois P. Heinz, Jul 29 2009

Status

approved