Thread: Triple Fibonacci Recursion

I'm certain the sequence for the recursive rule above is already popularized under some name (so what is it?)

Interesting properties? What about an explicit formula (I'm sure it'll include too)

Root 1	Root 2	Root 3	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10
0	0	1	1	2	4	6	12	22	40	74	136	250
0	1	0	1	2	3	6	11	20	37	68	125	230
1	0	0	1	1	2	4	7	13	24	44	81	149
1	5	10	16	31	57	104	192	353	649	1194	2196	4039
1	2	3	6	11	20	37	68	125	230	423	778	1431
			:P

Never mind. Tribonacci numbers (how did I not catch that?).

A systematic way to get explicit expressions out of a recursion relation is the z-transform: Z-transform - Wikipedia, the free encyclopedia