login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053633 Triangular array T(n,k) giving coefficients in expansion of Product_{j=1..n} (1+x^j) mod x^(n+1)-1. 6
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; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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).

REFERENCES

B. D. Ginsburg, On a number theory function applicable in coding theory, Problemy Kibernetiki, No. 19 (1967), pp. 249-252.

LINKS

Seiichi Manyama, Rows n = 0..139, flattened

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan 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 Allan 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

Index entries for sequences related to Gijswijt's sequence

FORMULA

The Maple code gives an explicit formula.

EXAMPLE

Triangle begins:

  k  0    1    2    3    4    5    6    7    8    9

n

0    1;

1    1,   1;

2    2,   1,   1;

3    2,   2,   2,   2;

4    4,   3,   3,   3,   3;

5    6,   5,   5,   6,   5,   5;

6   10,   9,   9,   9,   9,   9,   9;

7   16,  16,  16,  16,  16,  16,  16,  16;

8   30,  28,  28,  29,  28,  28,  29,  28,  28;

9   52,  51,  51,  51,  51,  52,  51,  51,  51,  51;

    ...

[Edited by Seiichi Manyama, Mar 11 2018]

MAPLE

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;

MATHEMATICA

Flatten[ Table[ CoefficientList[ PolynomialMod[ Product[1+x^j, {j, 1, n}], x^(n+1)-1], x], {n, 0, 11}]] (* Jean-Fran├žois Alcover, May 04 2011 *)

CROSSREFS

Cf. A053632, A063776, A300328, A300628. Leading coefficients give A000016, next column gives A000048.

Sequence in context: A134337 A261733 A268341 * A216460 A156755 A090822

Adjacent sequences:  A053630 A053631 A053632 * A053634 A053635 A053636

KEYWORD

tabl,nonn,easy,nice

AUTHOR

N. J. A. Sloane, Mar 22 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 22:51 EST 2019. Contains 319251 sequences. (Running on oeis4.)