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Search: id:A077947
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| A077947 |
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Expansion of 1/(1-x-x^2-2*x^3). |
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+0
13
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| 1, 1, 2, 5, 9, 18, 37, 73, 146, 293, 585, 1170, 2341, 4681, 9362, 18725, 37449, 74898, 149797, 299593, 599186, 1198373, 2396745, 4793490, 9586981, 19173961, 38347922, 76695845, 153391689, 306783378, 613566757, 1227133513, 2454267026, 4908534053, 9817068105
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=number of sequences of codewords of total length n from the code C={0,10,110,111}. E.g. a(3)=5 corresponds to the sequences 000, 010, 100, 110 and 111. - Paul Barry (pbarry(AT)wit.ie), Jan 23 2004
Diagonal sums of number Pascal-(1,2,1) triangle A081577. - Paul Barry (pbarry(AT)wit.ie), Jan 24 2005
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REFERENCES
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S. Roman, Introduction to Coding and Information Theory, Springer-Verlag, 1996, p. 42
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FORMULA
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a(n)=4*2^n/7+3cos(2*pi*n/3)/7+sqrt(3)sin(2*pi*n/3)/21 - Paul Barry (pbarry(AT)wit.ie), Jan 23 2004
Convolution of A000079 and A049347. a(n)=sum{k=0..n, 2^k*2sqrt(3)cos(2*pi(n-k)/3+pi/6)/3}. - Paul Barry (pbarry(AT)wit.ie), May 19 2004
a(n)=a(n-1)+a(n-2)+2a(n-3). - Paul Curtz (bpcrtz(AT)free.fr), May 23 2008
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CROSSREFS
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Apart from signs, same as A077972.
Cf. A139217 and A139218.
Sequence in context: A103422 A097281 A068036 this_sequence A077972 A152546 A085410
Adjacent sequences: A077944 A077945 A077946 this_sequence A077948 A077949 A077950
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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