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A031362 Number of coincidence site modules of index 10n+1 with 10-fold symmetry in plane. 0
1, 4, 0, 4, 4, 0, 4, 4, 0, 0, 4, 0, 8, 4, 0, 4, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 0, 4, 16, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 16, 4, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4, 16, 0, 4, 4, 0, 0, 0, 0, 4, 4, 0, 16, 0, 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 8, 4, 0, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Dirichlet g.f. is Sum_{n>=0} a(n+1)/(1+10n)^s. - R. J. Mathar, Jul 16 2010

REFERENCES

M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.

LINKS

Table of n, a(n) for n=1..100.

FORMULA

Dirichlet series: Product ((1+p^(-s))/(1-p^(-s)))^2 (p=1 mod 5).

MAPLE

read("transforms") : maxOrd := 1000 :

ZetaNum := proc(p, nmax, f) local n ; L := [1, seq(0, n=2..p-1), f, seq(0, n=p+1..nmax)] ; end proc:

Zeta := proc(p, nmax, f) local L, e; L := [1, seq(0, n=2..nmax)] ; for e from 1 do if p^e > nmax then break; else L := subsop(p^e=f^e, L) ; end if; end do: L ; end proc:

Zetap := [1, seq(0, n=2..maxOrd)] : for e from 1 to maxOrd by 5 do if isprime(e) then ZetaNum(e, maxOrd, 1) ; Zetap := DIRICHLET(Zetap, %) ; Zeta(e, maxOrd, 1) ; Zetap := DIRICHLET(Zetap, %) ; end if; end do:

Zetap := DIRICHLET(Zetap, Zetap) ; seq( Zetap[1+10*e], e=0..(nops(Zetap)-1)/10) ;

# R. J. Mathar, Jul 16 2010

CROSSREFS

Sequence in context: A016680 A062524 A152856 * A198414 A110854 A278086

Adjacent sequences:  A031359 A031360 A031361 * A031363 A031364 A031365

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from R. J. Mathar, Jul 16 2010

STATUS

approved

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Last modified July 17 23:21 EDT 2019. Contains 325109 sequences. (Running on oeis4.)