A298788 -id:A298788

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A298790

Partial sums of A298788.

+20
3

1, 4, 11, 23, 36, 53, 77, 100, 127, 163, 196, 233, 281, 324, 371, 431, 484, 541, 613, 676, 743, 827, 900, 977, 1073, 1156, 1243, 1351, 1444, 1541, 1661, 1764, 1871, 2003, 2116, 2233, 2377, 2500, 2627, 2783, 2916, 3053, 3221, 3364, 3511, 3691, 3844, 4001, 4193

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

FORMULA

Conjectures from Colin Barker, Jan 29 2018: (Start)

G.f.: (1 + x)^2*(1 + x + 4*x^2 + x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)^2).

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

(End)

CROSSREFS

Cf. A298788.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 27 2018

EXTENSIONS

More terms from Rémy Sigrist, Jan 28 2018

STATUS

approved

A298789

Coordination sequence for bey tiling (or net) with respect to a tetravalent node.

+10
3

1, 4, 7, 10, 15, 18, 20, 26, 29, 30, 37, 40, 40, 48, 51, 50, 59, 62, 60, 70, 73, 70, 81, 84, 80, 92, 95, 90, 103, 106, 100, 114, 117, 110, 125, 128, 120, 136, 139, 130, 147, 150, 140, 158, 161, 150, 169, 172, 160, 180, 183, 170, 191, 194, 180, 202, 205, 190

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

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

Rémy Sigrist, Illustration of the first terms

Rémy Sigrist, PARI program for A298789

FORMULA

Conjectures from Colin Barker, Jan 29 2018: (Start)

G.f.: (1 + x)^4*(1 + x^2) / ((1 - x)^2*(1 + x + x^2)^2).

a(n) = 2*a(n-3) - a(n-6) for n>6.