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A182191
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a(n) = 6*a(n-1) - a(n-2) + 12 with n>1, a(0)=-1, a(1)=5.
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3
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-1, 5, 43, 265, 1559, 9101, 53059, 309265, 1802543, 10506005, 61233499, 356895001, 2080136519, 12123924125, 70663408243, 411856525345, 2400475743839, 13990997937701, 81545511882379, 475282073356585, 2770146928257143, 16145599496186285, 94103450048860579
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OFFSET
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0,2
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COMMENTS
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If p is a prime of the form 8*r +/- 3 then a(p) == 1 (mod p); if p is a prime of the form 8*r +/- 1 then a(p) == 5 (mod p).
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 0..100
Index to sequences with linear recurrences with constant coefficients, signature (7,-7,1).
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FORMULA
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G.f.: -(1-12*x-x^2)/((1-x)*(1-6*x+x^2)). [Bruno Berselli, May 15 2012]
a(n) = 2*A038723(n)-3. [Bruno Berselli, May 16 2012]
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MATHEMATICA
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m = 19; n = 1; c = 0;
list3 = Reap[While[c < 22, t = 6 n - m + 12; Sow[t]; m = n; n = t; c++]][[2, 1]]
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PROG
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(MAGMA) I:=[-1, 5]; [n le 2 select I[n] else 6*Self(n-1)-Self(n-2)+12: n in [1..19]]; // Bruno Berselli, May 15 2012
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CROSSREFS
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Cf. A038723.
Sequence in context: A173554 A126963 A221874 * A038140 A178826 A082311
Adjacent sequences: A182188 A182189 A182190 * A182192 A182193 A182194
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KEYWORD
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sign,easy
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AUTHOR
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Kenneth J Ramsey, Apr 17 2012
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STATUS
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approved
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