A302241 Triangle T(n,k) read by rows giving the coefficients of the matching-generating polynomial of the n X n knight graph (0 <= k <= floor(n^2/2)).

1, 1, 1, 8, 20, 16, 2, 1, 24, 224, 1032, 2464, 2944, 1592, 320, 16, 1, 48, 964, 10592, 70024, 289344, 754244, 1226288, 1203410, 670000, 189544, 22112, 644, 1, 80, 2828, 58432, 786982, 7298848, 48033800, 227891056, 784428297, 1956801264, 3509779148, 4458911088, 3919123796, 2301829920, 858287984, 187915392, 21263600, 980608, 10304

Offset

1,4

Links

Table of n, a(n) for n=1..48.

Eric Weisstein's World of Mathematics, Knight Graph

Eric Weisstein's World of Mathematics, Matching-Generating Polynomial

Example

Rows as polynomials:
1,
1,
1 + 8*x + 20*x^2 + 16*x^3 + 2*x^4,
1 + 24*x + 224*x^2 + 1032*x^3 + 2464*x^4 + 2944*x^5 + 1592*x^6 + 320*x^7 + 16*x^8,
1 + 48*x + 964*x^2 + 10592*x^3 + 70024*x^4 + 289344*x^5 + 754244*x^6 + 1226288*x^7 + 1203410*x^8 + 670000*x^9 + 189544*x^10 + 22112*x^11 + 644*x^12,
...

Crossrefs

Row sums are A287225.

Sequence in context: A334065 A128909 A115147 * A022700 A214457 A205226

Adjacent sequences: A302238 A302239 A302240 * A302242 A302243 A302244

Keyword

nonn,tabl

Author

Eric W. Weisstein, Apr 03 2018

Status

approved