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A031362
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Number of coincidence site modules of index 10n+1 with 10-fold symmetry in plane.
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0
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| The Dirichlet g.f. is sum_{n>=0} a(n+1)/(1+10n)^s. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2010]
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REFERENCES
| M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.
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FORMULA
| Dirichlet series: Product ((1+p^(-s))/(1-p^(-s)))^2 (p=1 mod 5).
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MAPLE
| Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2010: (Start)
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) ; (End)
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CROSSREFS
| Sequence in context: A016680 A062524 A152856 * A198414 A110854 A021716
Adjacent sequences: A031359 A031360 A031361 * A031363 A031364 A031365
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2010
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