A182792 Number of n-colorings of the 7 X 7 X 7 triangular grid.

0, 0, 0, 6, 22665216, 3013780700340, 14668353488732160, 10142843465859326250, 2047585083571827265536, 177922459478738381782536, 8379024937788205785415680, 247855358008532074713890670, 5089690042011600555045120000

Offset: 0

Author

Alois P. Heinz, Dec 02 2010

Keywords

• nonn
• easy

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

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Chromatic polynomial
• Wikipedia, Triangular grid graph
• 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).

Crossrefs

7th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182791, A182793, A182794, A182795, A182796.

Programs

Maple

a:= n-> n^28 -63*n^27 +1917*n^26 -37515*n^25 +530415*n^24 -5770367*n^23 [phone]*n^22 -359161581*n^21 [phone]*n^20 -10907730408*n^19 [phone]*n^18 -177879720291*n^17 [phone]*n^16 -1637514420168*n^15 [phone]*n^14 -8685828617404*n^13 [phone]*n^12 -26442885506316*n^11 [phone]*n^10 -44834641208000*n^9 [phone]*n^8 -39623922744400*n^7
[phone]*n^6 -16032767219808*n^5 [phone]*n^4 -2251430597120*n^3 [phone]*n^2 -46172626432*n: seq(a(n), n=0..30);

Formula

a(n) = n^28 -63*n^27 + ... (see Maple program).