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Search: id:A053633
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| A053633 |
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Triangular array T(n,k) giving coefficients in expansion of Product_{j=1..n} (1+x^j) mod x^(n+1)-1. |
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5
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| 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 4, 3, 3, 3, 3, 6, 5, 5, 6, 5, 5, 10, 9, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 16, 30, 28, 28, 29, 28, 28, 29, 28, 28, 52, 51, 51, 51, 51, 52, 51, 51, 51, 51, 94, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 172, 170, 170, 172, 170, 170, 172
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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T(n,k) = number of binary vectors (x_1,...x_n) satisfying Sum_{i=1..n} i*x_i = k (mod n+1) = size of Varshamov-Tenengolts code VT_k(n).
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REFERENCES
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B. D. Ginsburg, On a number theory function applicable in coding theory, Problemy Kibernetiki, No. 19 (1967), pp. 249-252.
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LINKS
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F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
N. J. A. Sloane, On single-deletion-correcting codes
Index entries for sequences related to subset sums modulo m
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FORMULA
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The Maple code gives an explicit formula.
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EXAMPLE
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1; 1,1; 2,1,1; 2,2,2,2; 4,3,3,3,3; 6,5,5,6,5,5; ...
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MAPLE
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with(numtheory): A053633 := proc(n, k) local t1, d; t1 := 0; for d from 1 to n do if n mod d = 0 and d mod 2 = 1 then t1 := t1+(1/(2*n))*2^(n/d)*phi(d)*mobius(d/gcd(d, k))/phi(d/gcd(d, k)); fi; od; t1; end;
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CROSSREFS
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Cf. A053632, A063776. Leading coefficients give A000016, next column gives A000048.
Adjacent sequences: A053630 A053631 A053632 this_sequence A053634 A053635 A053636
Sequence in context: A025829 A029285 A134337 this_sequence A156755 A090822 A091975
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KEYWORD
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tabl,nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 22 2000
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