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A182792
Number of n-colorings of the 7 X 7 X 7 triangular grid.
12
0, 0, 0, 6, 22665216, 3013780700340, 14668353488732160, 10142843465859326250, 2047585083571827265536, 177922459478738381782536, 8379024937788205785415680, 247855358008532074713890670, 5089690042011600555045120000
OFFSET
0,4
COMMENTS
The 7 X 7 X 7 triangular grid has 7 rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has 28 vertices and 63 edges altogether.
LINKS
Index entries for linear recurrences with constant coefficients, signature (29, -406, 3654, -23751, 118755, -475020, 1560780, -4292145, 10015005, -20030010, 34597290, -51895935, 67863915, -77558760, 77558760, -67863915, 51895935, -34597290, 20030010, -10015005, 4292145, -1560780, 475020, -118755, 23751, -3654, 406, -29, 1).
FORMULA
a(n) = n^28 -63*n^27 + ... (see Maple program).
MAPLE
a:= n-> n^28 -63*n^27 +1917*n^26 -37515*n^25 +530415*n^24 -5770367*n^23 +50229001*n^22 -359161581*n^21 +2149154827*n^20 -10907730408*n^19 +47421892719*n^18 -177879720291*n^17 +578605822984*n^16 -1637514420168*n^15 +4039146735437*n^14 -8685828617404*n^13 +16263806276269*n^12 -26442885506316*n^11 +37160408393135*n^10 -44834641208000*n^9 +46004737388704*n^8 -39623922744400*n^7
+28128173982016*n^6 -16032767219808*n^5 +7056432341248*n^4 -2251430597120*n^3 +463382611200*n^2 -46172626432*n: seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 02 2010
STATUS
approved