The 𝑚-Path Cover Polynomial of a Graph and a Model for General Coefficient Linear Recurrences

Table 1

𝑛⧵𝑚	1	2	3	4	5	6	7	8	9	10	⋯
1	1	1	1	1	1	1	1	1	1	1	⋯
2	1	3	3	3	3	3	3	3	3	3	⋯
3	1	4	7	7	7	7	7	7	7	7	⋯
4	1	7	11	15	15	15	15	15	15	15	⋯
5	1	11	21	26	31	31	31	31	31	31	⋯
6	1	18	39	51	57	63	63	63	63	63	⋯
7	1	29	71	99	113	120	127	127	127	127	⋯
8	1	47	131	191	223	239	247	255	255	255	⋯
9	1	76	241	367	439	475	493	502	511	511	⋯
10	1	123	443	708	863	943	983	1003	1013	1023	⋯
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮