Search: id:A053633
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%I A053633
%S A053633 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,
%T A053633 16,16,16,16,16,30,28,28,29,28,28,29,28,28,52,51,51,51,51,52,51,51,
%U A053633 51,51,94,93,93,93,93,93,93,93,93,93,93,172,170,170,172,170,170,172
%N A053633 Triangular array T(n,k) giving coefficients in expansion of Product_{j=1..n} 
               (1+x^j) mod x^(n+1)-1.
%C A053633 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).
%D A053633 B. D. Ginsburg, On a number theory function applicable in coding theory, 
               Problemy Kibernetiki, No. 19 (1967), pp. 249-252.
%H A053633 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and 
               A. R. Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. 
               Integer Sequences, Vol. 10 (2007), #07.1.2.
%H A053633 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 
               [<a href="http://www.research.att.com/~njas/doc/gijs.pdf">pdf</a>
               , <a href="http://www.research.att.com/~njas/doc/gijs.ps">ps</a>].
%H A053633 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/dijen.txt">
               On single-deletion-correcting codes</a>
%H A053633 <a href="Sindx_Su.html#subsetsums">Index entries for sequences related 
               to subset sums modulo m</a>
%F A053633 The Maple code gives an explicit formula.
%e A053633 1; 1,1; 2,1,1; 2,2,2,2; 4,3,3,3,3; 6,5,5,6,5,5; ...
%p A053633 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;
%Y A053633 Cf. A053632, A063776. Leading coefficients give A000016, next column 
               gives A000048.
%Y A053633 Sequence in context: A025829 A029285 A134337 this_sequence A156755 A090822 
               A091975
%Y A053633 Adjacent sequences: A053630 A053631 A053632 this_sequence A053634 A053635 
               A053636
%K A053633 tabl,nonn,easy,nice
%O A053633 0,4
%A A053633 N. J. A. Sloane (njas(AT)research.att.com), Mar 22 2000

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