A298793 Coordination sequence for the bil tiling (or net) with respect to a trivalent node of the second type.

1, 3, 6, 8, 12, 15, 17, 21, 24, 27, 29, 31, 37, 40, 41, 43, 46, 53, 54, 54, 59, 62, 67, 68, 70, 75, 75, 81, 84, 85, 89, 89, 97, 100, 99, 103, 104, 113, 114, 112, 119, 120, 127, 128, 128, 135, 133, 141, 144, 143, 149, 147, 157, 160, 157, 163, 162, 173, 174, 170

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 A298793

Formula

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

G.f.: (1 - x + x^2)*(1 + 3*x + 7*x^2 + 10*x^3 + 15*x^4 + 15*x^5 + 16*x^6 + 14*x^7 + 15*x^8 + 14*x^9 + 15*x^10 + 11*x^11 + 9*x^12 + 4*x^13 + x^14 - 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. A298792, A298794, A298795.

Sequence in context: A135731 A118335 A189630 * A077024 A338722 A185549

Adjacent sequences: A298790 A298791 A298792 * A298794 A298795 A298796

Keyword

nonn

Author

N. J. A. Sloane, Jan 27 2018

Extensions

More terms from Rémy Sigrist, Mar 30 2018

Status

approved