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A299898 Coordination sequence for "ftu" 3D tiling with respect to first type of node. 3

%I

%S 1,4,9,16,26,40,57,78,103,130,159,190,224,262,305,353,405,458,511,566,

%T 623,685,754,829,907,986,1065,1143,1224,1311,1405,1505,1609,1714,1818,

%U 1922,2028,2140,2258,2382,2511,2641,2771,2902,3035,3171,3313,3461,3613,3768,3925,4083,4242,4404,4570,4741,4917

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

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

%H Davide M. Proserpio, <a href="/A299898/b299898.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 = (-198*n^3-3934*n^2-22755*n)*a(n)+(-198*n^3-4330*n^2-26491*n)*a(n+1)+(-198*n^3-4726*n^2-30227*n)*a(n+2)+(-198*n^3-5122*n^2-33963*n)*a(n+3)+(-396*n^3-9452*n^2-60454*n)*a(n+4)

%F +(-396*n^3-10244*n^2-67926*n)*a(n+5)+(-396*n^3-11036*n^2-75398*n)*a(n+6)+(-198*n^3-7894*n^2-60115*n)*a(n+7)+(-198*n^3-8290*n^2-63851*n)*a(n+8)+(-4752*n^2-44832*n)*a(n+9)

%F +(-4752*n^2-44832*n)*a(n+10)+(198*n^3-818*n^2-22077*n)*a(n+11)+(198*n^3-422*n^2-18341*n)*a(n+12)+(396*n^3+3908*n^2+8150*n)*a(n+13)+(396*n^3+4700*n^2+15622*n)*a(n+14)+(396*n^3+5492*n^2+23094*n)*a(n+15)

%F +(198*n^3+2350*n^2+7811*n)*a(n+16)+(198*n^3+2746*n^2+11547*n)*a(n+17)+(198*n^3+3142*n^2+15283*n)*a(n+18)+(198*n^3+3538*n^2+19019*n)*a(n+19),

%F with a(0) = 1, a(1)= 4, a(2) = 9, a(3) = 16, a(4) = 26, a(5) = 40, a(6) = 57, a(7) = 78, a(8) = 103, a(9) = 130, a(10) = 159, a(11) = 190, a(12) = 224, a(13) = 262, a(14) = 305, a(15) = 353, a(16) = 405, a(17) = 458, a(18) = 511, a(19) = 566.

%Y Cf. A299900 (second type), A299899 (partial sums).

%K nonn

%O 0,2

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

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Last modified August 2 20:05 EDT 2021. Contains 346428 sequences. (Running on oeis4.)