By N. J. A. Sloane

ISBN-10: 012648550X

ISBN-13: 9780126485509

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REF AFAS 23(2) 117 1894. LE1 79. ST4. MTAC 19 332 65. 78 1 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 5 , 5 , 5 , 6 , 7 , 8 , 8 , 9 , 11, 12, 12, 14, 16, 17, 18,20,23,25,26, 29,33,35,37,41,46,49,52,57,63,68,72,78,87,93,98, 107, 117, 125, 133, 144 PARTITIONS INTO DISTINCT ODD PARTS. REF PLMS 42 553 36. CJM 4 383 52. GU4. 79 1 , 2 , 2 , 2 , 2 , 3 , 4 , 4 , 4 , 5 , 6 , 6 , 6 , 8 , 9 , 10, 10, 12, 13, 14, 14, 16, 1 9 , 2 0 , 2 1 , 2 3 , 2 6 , 27, 28, 31, 34, 37, 38, 43, 46, 49, 50, 55, 60, 63, 66, 71, 78, 81, 84, 90, 98, 104, 107, 116 PARTITIONS INTO SQUARES.

Withgf 00 1 + x + x2 + 2x3 + 2x4 + · · · = Π ( 1 + *')■ i= l The partitions of the even numbers into parts which are powers of two form the binary partition function b(n), seq. 378: 1, 2, 4, 6, 10, 14, 20, 26, 36, 46, . , with recurrence b{n) = b(n- 1) + b([in]). P(D = l 1 p(2) = 2 2, l 2 p(3) = 3 3, 21, l 3 p(4) = 5 4, 31, 2 2 , 21 2 , l 4 p(5) = 7 5 , 4 1 , 32, 31 2 , 2 2 1, 21 3 , l 5 p(6) = 11 6, 51, 42, 41 2 , 3 2 , 321, 31 3 , 23, 2 2 1 2 , 21 4 , l 6 p{l) 7, 61, 52, 51 2 , 43, 421, 41 3 , 3 2 1, 322, 321 2 , 31 4 , 2 3 1, 2 2 1 3 , 21 5 , l 7 = 15 Fig.

REF BE1 296. 133 1,2,2,6,8, 18,30,67, 127 BORON TREES. REF CAY 9 451. 134 1,2,2,6,9, 17,30,54,98, 183,341,645, 1220,2327,4451,8555, 16489,31859, 61717,119779, 232919, 453584, 884544, 1727213, 3376505, 6607371 POPULATION OF U**2 + 12V**2. REF MTAC 20 567 66. 135 1,2,2, 6, 9, 20, 37, 86, 183, 419 HYDROCARBONS. REF BS1 201. 136 1,2,2,6,14, 34, 82, 198, 478, 1154, 2786, 6726, 16238, 39202, 94642, 228486, 551614, 1331714, 3215042, 7761798, 18738638, 45239074, 109216786, 263672646 A(N) = 2A(N - 1) + A(N - 2).