A299894 Coordination sequence for "bar" 3D tiling with respect to first type of node.

1, 4, 8, 16, 27, 35, 48, 66, 83, 113, 146, 174, 203, 231, 267, 311, 365, 418, 466, 509, 556, 617, 691, 768, 833, 897, 954, 1021, 1110, 1197, 1280, 1372, 1457, 1535, 1639, 1755, 1856, 1950, 2064, 2165, 2275, 2405, 2513, 2635, 2745, 2871, 3010

Offset

0,2

Comments

First 127 terms computed by Davide M. Proserpio using ToposPro.

Links

Davide M. Proserpio, Table of n, a(n) for n = 0..127

V. A. Blatov, A. P. Shevchenko, D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Cryst. Growth Des. 2014, 14, 3576-3586.

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

Formula

Conjectured recurrence, found by gfun, using the command rec:=gfun[listtorec](t1, a(n)); (where t1 is a list of the initial terms) suggested by Paul Zimmermann. (Note: this should not be used to extend the sequence.)

a(n+1)=2*a(n+2)-2*a(n+3)+a(n+4)-a(n+7)+3*a(n+8)-4*a(n+9)+4*a(n+10)-2*a(n+11)+2*a(n+14) -4*a(n+15)+4*a(n+16)-3*a(n+17)+a(n+18)-a(n+21)+2*a(n+22)-2*a(n+23)+a(n+24),

with a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 17, a(4) = 28, a(5) = 41, a(6) = 56, a(7) = 73, a(8) = 93, a(9) = 117, a(10) = 146, a(11) = 180, a(12) = 216, a(13) = 253, a(14) = 291, a(15) = 329, a(16) = 369, a(17) = 414, a(18) = 466, a(19) = 524, a(20) = 586, a(21) = 650, a(22) = 712, a(23) = 773.

Crossrefs

Cf. A299896 (second type), A299895 (partial sums).

Sequence in context: A257278 A257279 A334151 * A339026 A025197 A008371

Adjacent sequences: A299891 A299892 A299893 * A299895 A299896 A299897

Keyword

nonn

Author

N. J. A. Sloane, Feb 21 2018

Status

approved