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A299898 Coordination sequence for "ftu" 3D tiling with respect to first type of node. 3
1, 4, 9, 16, 26, 40, 57, 78, 103, 130, 159, 190, 224, 262, 305, 353, 405, 458, 511, 566, 623, 685, 754, 829, 907, 986, 1065, 1143, 1224, 1311, 1405, 1505, 1609, 1714, 1818, 1922, 2028, 2140, 2258, 2382, 2511, 2641, 2771, 2902, 3035, 3171, 3313, 3461, 3613, 3768, 3925, 4083, 4242, 4404, 4570, 4741, 4917 (list; graph; refs; listen; history; text; internal format)
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 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 = (-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)

+(-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)

+(-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)

+(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),

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.

CROSSREFS

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

Sequence in context: A073171 A049739 A006508 * A009875 A265044 A266336

Adjacent sequences:  A299895 A299896 A299897 * A299899 A299900 A299901

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 22 2018

STATUS

approved

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Last modified September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)