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A100321 The trinomial transform (A027907) gives powers of 2, while the trinomial transform of this sequence shift one place left gives powers of 3. 1
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; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

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

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).

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)

CROSSREFS

Cf. A027907.

Sequence in context: A234696 A169949 A261984 * A324839 A219751 A121133

Adjacent sequences:  A100318 A100319 A100320 * A100322 A100323 A100324

KEYWORD

sign

AUTHOR

Paul D. Hanna, Nov 15 2004

STATUS

approved

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Last modified August 8 05:25 EDT 2020. Contains 336290 sequences. (Running on oeis4.)