A299900 - OEIS

%I #14 Jan 03 2021 21:03:36

%S 1,4,7,12,24,38,50,68,94,122,153,187,223,260,293,331,382,438,500,569,

%T 628,678,737,800,870,958,1051,1141,1227,1303,1382,1475,1568,1672,1797,

%U 1914,2023,2135,2236,2343,2471,2597,2731,2885,3026,3156,3296

%N Coordination sequence for "ftu" 3D tiling with respect to second type of node.

%C First 127 terms computed by _Davide M. Proserpio_ using ToposPro.

%C I have to say that I am not very confident about the conjectured g.f. below. We only have 128 terms, and the recurrence has 57 or so coefficients and 57 or so initial terms, and 114 is pretty close to 128. So not much of a safety margin. If the same g.f. still holds when we get 500 terms I will believe it. - _N. J. A. Sloane_, Jan 03 2021

%H Davide M. Proserpio, <a href="/A299900/b299900.txt">Table of n, a(n) for n = 0..127</a>

%H V. A. Blatov, A. P. Shevchenko, D. M. Proserpio, <a href="http://pubs.acs.org/doi/pdf/10.1021/cg500498k">Applied Topological Analysis of Crystal Structures with the Program Package ToposPro</a>, Cryst. Growth Des. 2014, 14, 3576-3586.

%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/ftu">The ftu tiling (or net)</a>

%F The following is a 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_.

%F Note: this should not be used to extend the sequence.

%F 0 = 10*a(n+28)-9*a(n+29)+8*a(n+30)-7*a(n+31)+7*a(n+32)-8*a(n+33)+9*a(n+34) -10*a(n+35)+10*a(n+36)-10*a(n+37)+9*a(n+38)-9*a(n+39) +9*a(n+40) -10*a(n+41)+10*a(n+42)-10*a(n+43)+9*a(n+44)-9*a(n+45)+9*a(n+46)

%F -9*a(n+47)+8*a(n+48)-7*a(n+49)+6*a(n+50)-5*a(n+51)+4*a(n+52) -3*a(n+53)+3*a(n+54) -3*a(n+55)+3*a(n+56)-2*a(n+57)+a(n+58)+10*a(n+20)-10*a(n+21)-a(n+5)+2*a(n+6)-3*a(n+7)+3*a(n+8)-3*a(n+9)+3*a(n+10) -4*a(n+11

%F +5*a(n+12)-6*a(n+13)+7*a(n+14)-8*a(n+15)+9*a(n+16)-9*a(n+17)+9*a(n+18) -9*a(n+19)+10*a(n+22)-9*a(n+23)+9*a(n+24)-9*a(n+25)+10*a(n+26)-10*a(n+27), with

%F a(0) = 1, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 24, a(5) = 38, a(6) = 50, a(7) = 68, a(8) = 94, a(9) = 122, a(10) = 153, a(11) = 187, a(12) = 223, a(13) = 260, a(14) = 293, a(15) = 331, a(16) = 382, a(17) = 438, a(18) = 500, a(19) =569, a(20) = 628, a(21) = 678, a(22) = 737, a(23) = 800, a(24) = 870,

%F a(25) = 958, a(26) = 1051, a(27) = 1141, a(28) = 1227, a(29) = 1303, a(30) = 1382, a(31) = 1475, a(32) = 1568, a(33) = 1672, a(34) = 1797, a(35) = 1914, a(36) = 2023, a(37) = 2135, a(38) = 2236, a(39) = 2343, a(40) = 2471, a(41) = 2597, a(42) = 2731,

%F a(43) = 2885, a(44) = 3026, a(45) = 3156, a(46) = 3296, a(47) = 3429, a(48) = 3564, a(49) = 3722, a(50) = 3883, a(51) = 4048, a(52) = 4222, a(53) = 4381, a(54) = 4542, a(55) = 4718, a(56) = 4877, a(57) = 5041}.

%Y Cf. A299898 (first type), A299901 (partial sums).

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Feb 22 2018