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A155116
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a(n)=3*a(n-1)+3*a(n-2), n>2 ; a(0)=1, a(1)=2, a(2)=8.
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4
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1, 2, 8, 30, 114, 432, 1638, 6210, 23544, 89262, 338418, 1283040, 4864374, 18442242, 69919848, 265086270, 1005018354, 3810313872, 14445996678, 54768931650, 207644784984, 787241149902, 2984657804658, 11315696863680, 42901064005014
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 14 2010: (Start)
A berserker sequence, see A180140 and A180147. For the central square 16 A[5] vectors with decimal values between 3 and 384 lead to this sequence. These vectors lead for the corner squares to A123620 and for the side squares to A180142.
This sequence belongs to a family of sequences with GF(x)=(1-(2*k-1)*x-k*x^2)/(1-3*x+(k-4)*x^2). Berserker sequences that are members of this family are A000007 (k=2), A155116 (k=1; this sequence), A000302 (k=0), 6*A179606 (k=-1; with leading 1 added) and 2*A180141 (k=-2; n>=1 and a(0)=1). Some other members of this family are (-2)*A003688 (k=3; with leading 1 added), (-4)*A003946 (k=4; with leading 1 added), (-6)*A002878 (k=5; with leading 1 added) and (-8)*A033484 (k=6; with leading 1 added).
Inverse binomial transform of A101368 (without the first leading 1).
(End)
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,3).
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FORMULA
| G.f.: (1-x-x^2)/(1-3*x-3*x^2). a(n)=2*A125145(n-1), n>=1 .
a(n)=(2+4*A)*A^(-n-1)/21+(2+4*B)*B^(-n-1)/21 with A=(-3+sqrt(21))/6 and B=(-3-sqrt(21))/6 for n>=1 with a(0)=1.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 14 2010: (Start)
a(n) = A123620(n)/2 for n>=1.
(End)
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PROG
| (PARI) Vec((1-x-x^2)/(1-3*x-3*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012
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CROSSREFS
| Sequence in context: A052530 A162551 A073663 * A133915 A150759 A150760
Adjacent sequences: A155113 A155114 A155115 * A155117 A155118 A155119
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KEYWORD
| nonn,easy
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 20 2009
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EXTENSIONS
| Formula corrected by Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 12 2010
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