Row approach for the row 4, 4, 7, X, 103

F(n) = (a + b*n)*F(n-1) + c + d*n with F(0) = 4

Applied accordingly it results:
F(1) = (a + 1b)*F(0) + c + 1d = 4a + 4b + c + d = 4
F(2) = (a + 2b)*F(1) + c + 2d = 4a + 8b + c + 2d = 7
F(3) = (a + 3b)*F(2) + c + 3d = 7a + 21b + c + 3d = X
F(4) = (a + 4b)*F(3) + c + 4d = Xa + 4Xb + c + 4d = 103

Solving this system of equations delivers the parameters depending on X:
a = (4X² - 56X - 650) / (3X - 12)
b = (-X² + 14X + 230) / (3X - 12)
c = (-16X² + 227X + 2588) / (3X- 12)
d = (4X² - 47X - 956) / (3X - 12)

Anyhow, so you get solutions for nine whole-numbered X with whole-numbered continuations after the 103:

					n
X	a	b	c	d	5	6	7	8	9	10
7	-94	31	377	-121	6055	556711	68474983	10545146791	1950852155623	421384065613735
10	-45	15	181	-57	2986	134209	8052322	603923875	54353148418	5707080583501
13	-26	9	105	-33	1897	53023	1961725	90239191	4963155313	317641939807
19	-6	3	25	-9	907	10855	162787	2930119	61532443	1476778567
22	1	1	-3	-1	610	4261	34078	306691	3066898	33735865
31	18	-11/3	-71	53/3	-17	103	-737	8423	-126257	2356903
34	23	-5	-91	23	-182	1321	-15782	268387	-5904398	159418885
49	46	-11	-183	47	-875	17599	-545423	22907959	-1214121587	77703781855
94	109	-27	-435	111	-2558	135805	-10864058	1162454659	-155768923742	25078796723137

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