Discrete Mathematics with Graph Theory (3rd Edition) 135

Discrete - Section 5.2 133 P(8 = f(13 =[4(13 1l/3 = 17 f6(8 = f(17 =[4(17 1 l/3 = 23 F(8 = f(23 =[4(23 1 l/3 = 31 f8(8 = f(31 =[4(31 1l/3 = 41 f9(8

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Section 5.2 P(8) = f(13) = [4(13) -1l/3 = 17; f6(8) = f(17) = [4(17) + 1l/3 = 23; F(8) = f(23) = [4(23) + 1l/3 = 31; f8(8) = f(31) = [4(31) - 1l/3 = 41; f9(8) = f(41) = [4(41) + 1l/3 = 55; PO(8) = f(55) = [4(55) - 1]/3 = 73. 133 17. For n = 341, the values are gl(341) = 512, g2(341) = g(512) = 256, g3(341) = 128, g4(341) = 64, g5(341) = 32, g6(341) = 16, g7(341) = 8, g8(341) = 4, g9(341) = 2, glO(341) = 1. For m = 96, the values of gn(m) are gl(96) = g(96) = 96/2 = 48, g2(96) = g(48) = 24, g3(96) = g(24) = 12, g4(96) = g(12) = 6, g5(96) = g(6) = 3, g6(96) = g(3) = [3(3) + 1l/2 = 5, g7 (96) = g(5) = [3(5) + 1l/2 = 8, g8(96) = g(8) = 4, g9(96) = g(4) = 2, glO(96) = g(2) = 1. Similarly, for m = 104, the values of gn(m) are 52, 26,13,20,10,5,8,4,2,1; for m = 336, the values of gn(m) are 168,84,42,21,32,16,8,4,2,1; and for m = 133, the values are 200, 100,50,25,38,19,29,44,22,11,17,26, 13,20,10,5,8,4,2,1. 18. (a) [BB] The first ten terms are 2, 5, 8,11,14,17,20,23,26,29. The 123rd term is 2
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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