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A299900 Coordination sequence for "ftu" 3D tiling with respect to second type of node. 3
1, 4, 7, 12, 24, 38, 50, 68, 94, 122, 153, 187, 223, 260, 293, 331, 382, 438, 500, 569, 628, 678, 737, 800, 870, 958, 1051, 1141, 1227, 1303, 1382, 1475, 1568, 1672, 1797, 1914, 2023, 2135, 2236, 2343, 2471, 2597, 2731, 2885, 3026, 3156, 3296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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

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 ftu tiling (or net)

FORMULA

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.

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

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)

-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

+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

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,

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,

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}.

CROSSREFS

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

Sequence in context: A208668 A243860 A322619 * A215329 A208724 A183336

Adjacent sequences:  A299897 A299898 A299899 * A299901 A299902 A299903

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 22 2018

STATUS

approved

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Last modified May 9 20:59 EDT 2021. Contains 343746 sequences. (Running on oeis4.)