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# 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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