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

Author

N. J. A. Sloane, Jun 28 2002

Keywords

• nonn
• easy

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)

Crossrefs

Cf. A072150-A072154.

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

Extensions

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

Extended by Joseph Myers, Sep 29 2011