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A100321
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The trinomial transform (A027907) gives powers of 2, while the trinomial transform of this sequence shift one place left gives powers of 3.
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1
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1, 1, 0, 2, -3, 8, -16, 35, -72, 150, -307, 628, -1276, 2587, -5228, 10546, -21235, 42704, -85784, 172179, -345344, 692286, -1387155, 2778492, -5563748, 11138443, -22294596, 44617850, -89282067, 178639160, -357399712, 714995843, -1430309496, 2861133222, -5723098483, 11447543236
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| G.f.: (1 + 3*x - 3*x^3)/(1 + 2*x - 2*x^2 - 3*x^3 + 2*x^4). 2^n = Sum_{k=0..2*n} A027907(n, k)*a(k); 3^n = Sum_{k=0..2*n} A027907(n, k)*a(k+1).
a(n) = (1/3) [(-1)^n * (3*Fib(n-1) - 2^n) + 1 ]. - Ralf Stephan, May 15 2007
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EXAMPLE
| 2^3 = 1*(1) + 3*(1) + 6*(0) + 7*(2) + 6*(-3) + 3*(8) + 1*(-16).
3^3 = 1*(1) + 3*(0) + 6*(2) + 7*(-3) + 6*(8) + 3*(-16) + 1*(35).
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PROG
| (PARI) a(n)=polcoeff((1+3*x-3*x^3)/(1+2*x-2*x^2-3*x^3+2*x^4+x*O(x^n)), n)
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CROSSREFS
| Cf. A027907.
Sequence in context: A153699 A182670 A169949 * A121133 A011952 A032104
Adjacent sequences: A100318 A100319 A100320 * A100322 A100323 A100324
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 15 2004
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