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Triangle read by rows: coefficients of the edge cover polynomial for the n-path graph P_n.
4

%I #16 Jun 05 2017 23:09:43

%S 0,0,1,0,0,1,0,0,1,1,0,0,0,2,1,0,0,0,1,3,1,0,0,0,0,3,4,1,0,0,0,0,1,6,

%T 5,1,0,0,0,0,0,4,10,6,1,0,0,0,0,0,1,10,15,7,1,0,0,0,0,0,0,5,20,21,8,1,

%U 0,0,0,0,0,0,1,15,35,28,9,1,0,0,0,0,0,0,0,6,35,56,36,10,1,0,0,0,0,0,0,0,1,21,70,84,45,11,1

%N Triangle read by rows: coefficients of the edge cover polynomial for the n-path graph P_n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EdgeCoverPolynomial.html">Edge Cover Polynomial</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PathGraph.html">Path Graph</a>

%F a(n) = abs(A057094(n)).

%e 0;

%e 0,1;

%e 0,0,1;

%e 0,0,1,1;

%e 0,0,0,2,1;

%e 0,0,0,1,3,1;

%e 0,0,0,0,3,4,1;

%e 0,0,0,0,1,6,5,1;

%e 0,0,0,0,0,4,10,6,1;

%e 0,0,0,0,0,1,10,15,7,1;

%e 0,0,0,0,0,0,5,20,21,8,1;

%e 0,0,0,0,0,0,1,15,35,28,9,1;

%e 0,0,0,0,0,0,0,6,35,56,36,10,1;

%e 0,0,0,0,0,0,0,1,21,70,84,45,11,1;

%e ...

%t Prepend[CoefficientList[Table[x^(n/2) Fibonacci[n - 1, Sqrt[x]], {n, 2, 14}], x], {0}] // Flatten (* _Eric W. Weisstein_, Apr 06 2017 *)

%t Prepend[CoefficientList[LinearRecurrence[{x, x}, {0, x}, {2, 14}], x], {0}] // Flatten (* _Eric W. Weisstein_, Apr 07 2017 *)

%Y Unsigned version of A057094.

%Y Row sums are A000045(n-1).

%Y Cf. A286912, A258993, A030528, A085478, A098925, A102426, A143858, etc.

%K nonn,tabl,easy

%O 1,14

%A _Eric W. Weisstein_, Apr 06 2017