A298792 Coordination sequence for the bil tiling (or net) with respect to a trivalent node of the first type.

1, 3, 6, 9, 11, 14, 19, 22, 23, 25, 30, 35, 35, 36, 41, 46, 49, 49, 52, 57, 60, 63, 64, 67, 71, 74, 79, 80, 81, 85, 90, 95, 93, 94, 101, 106, 109, 107, 110, 117, 120, 123, 122, 125, 131, 134, 139, 138, 139, 145, 150, 155, 151, 152, 161, 166, 169, 165, 168, 177

Offset

0,2

Links

Rémy Sigrist, Table of n, a(n) for n = 0..1000

Reticular Chemistry Structure Resource (RCSR), The bil tiling (or net)

Rémy Sigrist, Illustration of first terms

Rémy Sigrist, PARI program for A298792

Formula

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

G.f.: (1 + 2*x + 5*x^2 + 7*x^3 + 10*x^4 + 12*x^5 + 15*x^6 + 14*x^7 + 16*x^8 + 14*x^9 + 15*x^10 + 12*x^11 + 10*x^12 + 7*x^13 + 5*x^14 + 2*x^15 + x^16) / ((1 - x)^2*(1 + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)^2).

a(n) = a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 3*a(n-5) - 3*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 3*a(n-10) + 3*a(n-11) - 2*a(n-12) + 2*a(n-13) - 2*a(n-14) + a(n-15) - a(n-16) for n>16.

(End)

Prog

(PARI) See Links section.

Crossrefs

Cf. A298793, A298794, A298795.

Sequence in context: A151926 A166265 A145283 * A177800 A310147 A310148

Adjacent sequences: A298789 A298790 A298791 * A298793 A298794 A298795

Keyword

nonn

Author

N. J. A. Sloane, Jan 27 2018

Extensions

More terms from Rémy Sigrist, Mar 30 2018

Status

approved