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 A212208 Triangle T(n,k), n>=1, 0<=k<=n^2, read by rows: row n gives the coefficients of the chromatic polynomial of the square diagonal grid graph DG_(n,n), highest powers first. 19
 1, 0, 1, -6, 11, -6, 0, 1, -20, 174, -859, 2627, -5082, 6048, -4023, 1134, 0, 1, -42, 825, -10054, 85011, -528254, 2491825, -9084089, 25795983, -57031153, 97292827, -125639547, 118705077, -77301243, 30931875, -5709042, 0, 1, -72, 2492, -55183, 877812 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The square diagonal grid graph DG_(n,n) has n^2 = A000290(n) vertices and 2*(n-1)*(2*n-1) = A002943(n-1) edges. The chromatic polynomial of DG_(n,n) has n^2+1 = A002522(n) coefficients. LINKS Alois P. Heinz, Rows n = 1..7, flattened Wikipedia, Chromatic Polynomial EXAMPLE 3 example graphs:                          o---o---o .                                          |\ /|\ /| .                                          | X | X | .                                          |/ \|/ \| .                             o---o        o---o---o .                             |\ /|        |\ /|\ /| .                             | X |        | X | X | .                             |/ \|        |/ \|/ \| .                o            o---o        o---o---o Graph:        DG_(1,1)       DG_(2,2)       DG_(3,3) Vertices:        1              4              9 Edges:           0              6             20 The square diagonal grid graph DG_(2,2) equals the complete graph K_4 and has chromatic polynomial q*(q-1)*(q-2)*(q-3) = q^4 -6*q^3 +11*q^2 -6*q => row 2 = [1, -6, 11, -6, 0]. Triangle T(n,k) begins: 1,    0; 1,   -6,    11,      -6,        0; 1,  -20,   174,    -859,     2627,      -5082, ... 1,  -42,   825,  -10054,    85011,    -528254, ... 1,  -72,  2492,  -55183,   877812,  -10676360, ... 1, -110,  5895, -205054,  5203946, -102687204, ... 1, -156, 11946, -598491, 22059705, -637802510, ... CROSSREFS Columns 1-2 give: A000012, (-1)*A002943(n-1). Row sums (for n>1) and last elements of rows give: A000004, row lengths give: A002522. Cf. A000290, A212209. Sequence in context: A009443 A258054 A106540 * A334280 A134012 A103704 Adjacent sequences:  A212205 A212206 A212207 * A212209 A212210 A212211 KEYWORD sign,tabf AUTHOR Alois P. Heinz, May 04 2012 STATUS approved

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Last modified September 30 11:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)