Shilla distance-regular graphs with b(2) = sc(2)

A Shilla graph is a distance-regular graph Gamma of diameter 3 whose second eigenvalue is a = a(3). A Shilla graph has intersection array {ab, (a + 1)(b - 1), b(2); 1, c(2), a(b - 1)}. J. Koolen and J. Park showed that, for a given number b, there exist only finitely many Shilla graphs. They also found all possible admissible intersection arrays of Shilla graphs for b is an element of {2, 3}. Earlier the author together with A. A. Makhnev studied Shilla graphs with b(2) = c(2). In the present paper, Shilla graphs with b(2) = sc(2), where s is an integer greater than 1, are studied. For Shilla graphs satisfying this condition and such that their second nonprincipal eigenvalue is - 1, five infinite series of admissible intersection arrays are found. It is shown that, in the case of Shilla graphs without triangles in which b(2) = sc(2) and b < 170, only six admissible intersection arrays are possible. For a Q-polynomial Shilla graph with b(2) = sc(2), admissible intersection arrays are found in the cases b = 4 and b = 5, and this result is used to obtain a list of admissible intersection arrays of Shilla graphs for b is an element of {4, 5} in the general case.