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A102702
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G.f. (2-x-2*x^2-x^3)/(x^4+2*x^3-x^2-2*x+1).
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0
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2, 3, 6, 10, 18, 31, 54, 93, 160, 274, 468, 797, 1354, 2295, 3882, 6554, 11046, 18587, 31230, 52401, 87812, 146978, 245736, 410425, 684818, 1141611, 1901454, 3164458, 5262330, 8744599, 14521158, 24097797, 39965224, 66241330, 109731132
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| A floretion-generated sequence which results from a certain transform of the Fibonacci numbers. Specifically, (a(n)) is the (type 1B) tesfor-transform of the Fibonacci numbers (A000045) with respect to the floretion + .5'i + .5i' Note, for example, that the sequence A001629, appearing in the formula given, has the name "Fibonacci numbers convolved with themselves" and that this sequence arises in FAMP (see program code) under the name: the lesfor-transform (type 1B) of the Fibonacci numbers (A000045) with respect to the floretion + .5'i + .5i' . The denominator of the generating function has roots at the golden ratio phi and -(1+phi).
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REFERENCES
| V. E. Hoggatt, Jr. and M. Bicknell-Johnson, Fibonacci convolution sequences, Fib. Quart., 15 (1977), 117-122.
Thomas Koshy, Fibonacci and Lucas Numbers with Applications, Chapter 15, page 187, "Hosoya's Triangle"
S. Vajda, Fibonacci and Lucas numbers and the Golden Section, Ellis Horwood Ltd., Chichester, 1989, p. 183, Nr.(98).
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n) = 2*F(n+1) + A001629(n+3) - 2*A029907(n+1); F(n+1) = a(n+2) - a(n+1) - a(n)
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PROG
| Floretion Algebra Multiplication Program. FAMP Code: (a(n)) = 2tesforseq[ + .5'i + .5i' ], 2lesforseq = A001629, jesforseq = A029907, vesforseq = A000045, ForType: 1B.
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CROSSREFS
| Cf. A001629, A029907, A000045.
Sequence in context: A066067 A121364 A172516 * A060945 A181532 A077930
Adjacent sequences: A102699 A102700 A102701 * A102703 A102704 A102705
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KEYWORD
| easy,nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Feb 04 2005
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 02 2006
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