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0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Period 6: repeat 0,1,4,9,4,1.
Occurs in Mariotte reference, pp.511-512. Consider waterjets of heights 0,5,10, ... = A008587 up to 100 pieds (feet). a(n) is the difference in pouces (inches) between tank's heights (in feet and inches) and part in feet (0,5,10,15,21,..). Row with 0's is implicit. [From Paul Curtz (bpcrtz(AT)free.fr), Nov 18 2008]
a(m*n)=a(m)*a(n) mod 12; a(6*n+k)=a(6*n-k) for k<=6*n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 24 2009]
Equivalently, n^4 mod 12. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 31 2009]
n^z mod 12, if z even number. Example:n^180 mod 12. etc... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2009]
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REFERENCES
| Mariotte, Regles pour les jets d'eau, pp. 508-518. In Divers ouvrages de mathematique et de physique par Messieurs de l'Academie Royale des Sciences, 6, 518, 1 p., Paris, 1693. Edme Mariotte (1620-1684) is known for the perfect gas law (1676, Essai sur l'air), but later than Robert Boyle (1662). [From Paul Curtz (bpcrtz(AT)free.fr), Nov 18 2008]
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FORMULA
| a(n)=(1/45)*{17*(n mod 6)+32*[(n+1) mod 6]+47*[(n+2) mod 6]-28*[(n+3) mod 6]-13*[(n+4) mod 6]+2*[(n+5) mod 6]}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 27 2008]
G.f.: -x*(1+4*x+9*x^2+4*x^3+x^4)/((x-1)*(1+x)*(1+x+x^2)*(x^2-x+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 23 2009]
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MATHEMATICA
| Table[Mod[n^2, 12], {n, 0, 200}] (* From Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
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PROG
| (Other) sage: [power_mod(n, 4, 12)for n in xrange(0, 101)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 31 2009]
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CROSSREFS
| A070431, A008959, A070438, A070442, A070452, A159852, A000290. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 24 2009]
Sequence in context: A070436 A178143 * A070516 A143298 A177839 A013669
Adjacent sequences: A070432 A070433 A070434 * A070436 A070437 A070438
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 12 2002
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