On 𝑘-Distance Pell Numbers in 3-Edge-Coloured Graphs

Table 1

The 𝑘-distance Pell sequence 𝑃_𝑘(𝑛).

𝑛	0	1	2	3	4	5	6	7	8	9	10	11	12	13
𝑃𝑛	0	1	2	5	12	29	70	169	408	985	2378	5741	13860	33461
𝑃3(𝑛)	0	1	2	4	9	20	44	97	214	472	1041	2296	5064	11169
𝑃4(𝑛)	0	1	2	4	8	17	36	76	160	337	710	1496	3152	6641
𝑃5(𝑛)	0	1	2	4	8	16	33	68	140	288	592	1217	2502	5144
𝑃6(𝑛)	0	1	2	4	8	16	32	65	132	268	514	1104	2240	4545