A284938 Triangle read by rows: coefficients of the edge cover polynomial for the n-path graph P_n.

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, 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, 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

Offset: 1

Author

Eric W. Weisstein, Apr 06 2017

Keywords

• nonn
• tabl
• easy

Examples

			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;
0,0,0,0,1,6,5,1;
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;
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;
...
		

Links

• Eric Weisstein's World of Mathematics, Edge Cover Polynomial
• Eric Weisstein's World of Mathematics, Path Graph

Crossrefs

Unsigned version of A057094.

Row sums are A000045(n-1).

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

Programs

Mathematica

Prepend[CoefficientList[Table[x^(n/2) Fibonacci[n - 1, Sqrt[x]], {n, 2, 14}], x], {0}] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)
Prepend[CoefficientList[LinearRecurrence[{x, x}, {0, x}, {2, 14}], x], {0}] // Flatten (* Eric W. Weisstein, Apr 07 2017 *)

Formula

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