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

0,2

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

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A301285.

Sequence in context: A310139 A350619 A341435 * A288218 A212984 A006048

Adjacent sequences: A301280 A301281 A301282 * A301284 A301285 A301286

Keyword

nonn

Author

N. J. A. Sloane, Mar 23 2018

Extensions

More terms from Rémy Sigrist, Mar 28 2018

Status

approved