A301283 Coordination sequence for node of type V1 in "car" 2-D tiling (or net).

1, 3, 6, 8, 12, 17, 18, 20, 26, 29, 29, 33, 39, 41, 41, 45, 52, 54, 52, 57, 66, 66, 63, 70, 79, 78, 75, 82, 92, 91, 86, 94, 106, 103, 97, 107, 119, 115, 109, 119, 132, 128, 120, 131, 146, 140, 131, 144, 159, 152, 143, 156, 172, 165, 154, 168, 186, 177, 165

Offset: 0

Author

N. J. A. Sloane, Mar 23 2018

Keywords

• nonn

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..1000
• Reticular Chemistry Structure Resource (RCSR), The car tiling (or net)
• Rémy Sigrist, PARI program for A301283
• Rémy Sigrist, Illustration of first terms

Crossrefs

Cf. A301285.

Programs

PARI

See Links section.

Formula

Conjectures from Colin Barker, Mar 30 2018: (Start)

G.f.: (1 + 2*x + 5*x^2 + 5*x^3 + 9*x^4 + 6*x^5 + 6*x^6 + 3*x^7 + x^8 - x^10) / ((1 - x)^2*(1 + x^2)^2*(1 + x + x^2)).

a(n) = a(n-1) - 2*a(n-2) + 3*a(n-3) - 2*a(n-4) + 3*a(n-5) - 2*a(n-6) + a(n-7) - a(n-8) for n>8.

(End)

Equivalent conjecture: 12*a(n) = 37*n+4*b(n)+6*(-1)^(n/2)*A142150(n+2)+3*c(n) for n>2, where b(n)=0,-1,1 (3-periodic, n>=0) and c(n) = -6,5,6,-5 (4-periodic, n>=0). - R. J. Mathar, Mar 31 2018

Extensions

More terms from Rémy Sigrist, Mar 28 2018