|
| |
|
|
A299273
|
|
Partial sums of A299272.
|
|
51
|
|
|
|
1, 7, 25, 62, 125, 224, 366, 555, 804, 1121, 1505, 1973, 2535, 3183, 3939, 4816, 5797, 6910, 8172, 9555, 11094, 12811, 14665, 16699, 18941, 21335, 23933, 26770, 29773, 33004, 36506, 40187, 44120, 48357, 52785, 57489, 62531, 67775, 73319, 79236, 85365, 91818, 98680, 105763, 113194, 121071, 129177
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1).
|
|
|
FORMULA
|
Conjectures from Colin Barker, Feb 11 2018: (Start)
G.f.: (1 + x)^3*(1 + x^2)*(1 + 3*x + 5*x^2 + 3*x^3 + x^4) / ((1 - x)^4*(1 + x + x^2)^3).
a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) - 3*a(n-6) + 3*a(n-7) + a(n-9) - a(n-10) for n>9.
(End)
These conjectures are correct. - N. J. A. Sloane, Feb 12 2018
|
|
|
MATHEMATICA
|
CoefficientList[Series[(1+x)^3*(1+x^2)*(1+3*x+5*x^2+3*x^3+x^4)/((1-x)^4*(1+x+x^2)^3), {x, 0, 50}], x] (* G. C. Greubel, Feb 20 2018 *)
|
|
|
PROG
|
(PARI) x='x+O('x^30); Vec((1+x)^3*(1+x^2)*(1+3*x+5*x^2+3*x^3+x^4)/((1-x)^4*(1+x+x^2)^3)) \\ G. C. Greubel, Feb 20 2018
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((1+x)^3*(1+x^2)*(1+3*x+5*x^2+3*x^3+x^4)/((1-x)^4*(1+x+x^2)^3))) // G. C. Greubel, Feb 20 2018
|
|
|
CROSSREFS
|
Cf. A299272.
The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e: A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.
Sequence in context: A330044 A193375 A185787 * A001845 A127765 A155305
Adjacent sequences: A299270 A299271 A299272 * A299274 A299275 A299276
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, Feb 10 2018
|
|
|
STATUS
|
approved
|
| |
|
|
