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A210695
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a(n) = 6*a(n-1) - a(n-2) + 6 with n>1, a(0)=0, a(1)=1.
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2
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0, 1, 12, 77, 456, 2665, 15540, 90581, 527952, 3077137, 17934876, 104532125, 609257880, 3551015161, 20696833092, 120629983397, 703083067296, 4097868420385, 23884127455020, 139206896309741, 811357250403432, 4728936606110857, 27562262386261716
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OFFSET
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0,3
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COMMENTS
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It appears that if p is a prime of the form 8*r +/- 1, a(p-1) == 0 (mod p); and that if p is a prime of the form 8*r +/- 3, a(p+1) == 0 (mod p).
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LINKS
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FORMULA
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a(n) = ((1-2*sqrt(2))*(1-sqrt(2))^(2n-1)+(1+2*sqrt(2))*(1+sqrt(2))^(2n-1)-6)/4. [Bruno Berselli, Jun 26 2012]
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MATHEMATICA
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m = 36; n = 5; c = 0;
list3 = Reap[While[c < 22, t = 6 n - m + 6; Sow[t]; m = n; n = t; c++]][[2, 1]]
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PROG
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(Magma) [n le 2 select n-1 else 6*Self(n-1)-Self(n-2)+6: n in [1..23]]; // Bruno Berselli, Jun 26 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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