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Search: id:A022166
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| A022166 |
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Triangle of Gaussian binomial coefficients [n,k] for q = 2. |
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+0
7
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| 1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 35, 15, 1, 1, 31, 155, 155, 31, 1, 1, 63, 651, 1395, 651, 63, 1, 1, 127, 2667, 11811, 11811, 2667, 127, 1, 1, 255, 10795, 97155, 200787, 97155, 10795, 255, 1, 1, 511, 43435, 788035
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Also number of distinct binary linear [n,k] codes.
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REFERENCES
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F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
D. Slepian, A class of binary signaling alphabets. Bell System Tech. J. 35 (1956), 203-234.
D. Slepian, Some further theory of group codes. Bell System Tech. J. 39 1960 1219-1252.
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LINKS
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T. D. Noe, Rows n=0..50 of triangle, flattened
Index entries for sequences related to binary linear codes
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FORMULA
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G.f.: A(x,y) = Sum_{k>=0} y^k/Product_{j=0..k} (1 - 2^j*x). - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2006
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 3, 1;
1, 7, 7, 1;
1, 15, 35, 15, 1;
1, 31, 155, 155, 31, 1;
1, 63, 651, 1395, 651, 63, 1;
1, 127, 2667, 11811, 11811, 2667, 127, 1;
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PROGRAM
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(PARI) T(n, k)=polcoeff(x^k/prod(j=0, k, 1-2^j*x+x*O(x^n)), n) - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2006
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CROSSREFS
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Row sums give A006116. Cf. A006516, A022167.
Central terms are A006098.
Sequence in context: A108470 A136126 A046802 this_sequence A058669 A057004 A059328
Adjacent sequences: A022163 A022164 A022165 this_sequence A022167 A022168 A022169
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KEYWORD
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nonn,tabl
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AUTHOR
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njas
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