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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A153731 Triangle read by rows: nonzero coefficients of Swinnerton-Dyer polynomials. 2
-2, 1, 1, -10, 1, 576, -960, 352, -40, 1, 46225, -5596840, 13950764, -7453176, 1513334, -141912, 6476, -136, 1, 2000989041197056, -44660812492570624, 183876928237731840, -255690851718529024, 172580952324702208 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Roman E. Maeder. Programming in Mathematica, Addison-Wesley, 1990, page 105.

LINKS

Table of n, a(n) for n=1..24.

Eric Weisstein's World of Mathematics, Swinnerton-Dyer Polynomial

EXAMPLE

First few rows are:

-2, 1;

1, -10, 1;

576, -960, 352, -40, 1;

46225, -5596840, 13950764, -7453176, 1513334, -141912, 6476, -136, 1;

....

-2 + x^2, 1 - 10*x^2 + x^4, 576 - 960*x^2 + 352*x^4 - 40*x^6 + x^8, ...

MATHEMATICA

SwinnertonDyerP[0, x_ ] := x; SwinnertonDyerP[n_, x_ ] := Module[{sd, srp = Sqrt[Prime[n]]}, sd[y_] = SwinnertonDyerP[n - 1, y]; Expand[ sd[x + srp] sd[x - srp] ] ]; row[n_] := CoefficientList[ SwinnertonDyerP[n, x], x^2]; Table[row[n], {n, 1, 5}] // Flatten (* Jean-Fran├žois Alcover, Nov 09 2012 *)

PROG

(Julia)

using Nemo

function A153731Row(n)

    R, x = PolynomialRing(ZZ, "x")

    p = swinnerton_dyer(n, x)

    [coeff(p, j) for j in 0:2:2^n] end

for n in 1:4 A153731Row(n) |> println end # Peter Luschny, Mar 13 2018

CROSSREFS

Sequence in context: A256168 A054768 A104251 * A262226 A298158 A154989

Adjacent sequences:  A153728 A153729 A153730 * A153732 A153733 A153734

KEYWORD

sign,tabf

AUTHOR

Eric W. Weisstein, Dec 31 2008

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified July 17 17:07 EDT 2018. Contains 312721 sequences. (Running on oeis4.)