A287376 Array read by antidiagonals: T(m,n) = number of independent vertex sets in the complete prism graph K_m X C_n.
1, 3, 1, 4, 7, 1, 7, 13, 13, 1, 11, 35, 34, 21, 1, 18, 81, 121, 73, 31, 1, 29, 199, 391, 325, 136, 43, 1, 47, 477, 1300, 1361, 731, 229, 57, 1, 76, 1155, 4285, 5781, 3771, 1447, 358, 73, 1, 123, 2785, 14161, 24473, 19606, 8881, 2605, 529, 91, 1
Offset: 1
Examples
Table starts: ==================================================== m\n| 1 2 3 4 5 6 7 8 ---|------------------------------------------------ 1 | 1 3 4 7 11 18 29 47 ... 2 | 1 7 13 35 81 199 477 1155 ... 3 | 1 13 34 121 391 1300 4285 14161 ... 4 | 1 21 73 325 1361 5781 24473 103685 ... 5 | 1 31 136 731 3771 19606 101781 528531 ... 6 | 1 43 229 1447 8881 54763 337429 2079367 ... 7 | 1 57 358 2605 18551 132504 946037 6754805 ... 8 | 1 73 529 4361 35361 287305 2333745 18957321 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1275
Crossrefs
Programs
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Mathematica
max = 10; row[m_] := ((m+1) - (m^2 - 2)*x - (2*m - 1)*x^2)/(1 - (m-1)*x - (m+1)*x^2 - x^3) + O[x]^(max+1) // CoefficientList[#, x]& // Rest; T = Table[row[m], {m, 1, max}]; Table[T[[m-n+1, n]], {m, 1, max}, {n, m, 1, -1}] // Flatten (* Jean-François Alcover, Jun 06 2017 *) -
PARI
RowGf(m,x)=((m+1)-(m^2-2)*x-(2*m-1)*x^2)/(1-(m-1)*x-(m+1)*x^2-x^3); for (m=1,8,for(n=1,8,print1(Vec(RowGf(m,x)+O(x^(n+1)))[n+1], " "));print);
Formula
Row g.f.: ((m+1)-(m^2-2)*x-(2*m-1)*x^2)/(1-(m-1)*x-(m+1)*x^2-x^3).
Comments