A072149 Coordination sequence for AlPO_4-11 structure with respect to node (X) where decagon and two hexagons meet.

1, 3, 6, 8, 10, 13, 16, 19, 20, 22, 28, 31, 30, 33, 38, 40, 42, 43, 46, 53, 54, 52, 58, 63, 62, 65, 68, 70, 76, 77, 76, 83, 86, 84, 90, 93, 92, 99, 102, 100, 106, 109, 108, 115, 116, 114, 124, 127, 122, 129, 134, 132, 138, 139, 138, 149, 150, 144, 154, 159

Offset

0,2

Comments

There are three types of nodes in this structure.

The coordination sequence with respect to a particular node gives the number of nodes that can be reached from that node in n steps along edges.

Links

Joseph Myers, Table of n, a(n) for n = 0..1000

M. E. Davis, Ordered porous materials for emerging applications, Nature, 417 (Jun 20 2002), 813-821 (gives structure).

N. J. A. Sloane, AlPO_4-11 structure, after Davis

R. J. Mathar, Illustration of counts and adjacencies (PostScript)

Formula

Empirical: G.f. 1 +x*(3 +6*x +11*x^2 +13*x^3 +15*x^4 +15*x^5 +16*x^6 +15*x^7 +15*x^8 +13*x^9 +11*x^10 +6*x^11 +3*x^12) / ( (1+x^2)*(x^6+x^3+1)*(x-1)^2*(1+x+x^2)^2 ) with a(n)= -a(n-2) +a(n-3) +a(n-5) +a(n-9) +a(n-11) -a(n-12) -a(n-14). - R. J. Mathar, Sep 30 2011

Crossrefs

Cf. A072150-A072154.

Sequence in context: A190325 A064437 A287180 * A001066 A099518 A280106

Adjacent sequences: A072146 A072147 A072148 * A072150 A072151 A072152

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 28 2002

Extensions

More terms from R. J. Mathar, Mar 29 2007

Extended by Joseph Myers, Sep 29 2011

Status

approved