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A101463
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G.f.: (x^3+x^2+2*x+1)/(x^4+5*x^2+1).
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0
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1, 2, -4, -9, 19, 43, -91, -206, 436, 987, -2089, -4729, 10009, 22658, -47956, -108561, 229771, 520147, -1100899, -2492174, 5274724, 11940723, -25272721, -57211441, 121088881, 274116482, -580171684, -1313370969, 2779769539, 6292738363, -13318676011
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A floretion-generated sequence relating to Pythagoras' theorem generalized.
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REFERENCES
| F. A. Haight, On a generalization of Pythagoras' theorem, pp. 73-77 of J. C. Butcher, editor, A Spectrum of Mathematics. Auckland University Press, 1971.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
James A. Sellers, Domino Tilings and Products of Fibonacci and Pell Numbers, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.2
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FORMULA
| Let b(1)=1, b(2)=2, b(3)=4 and b(n)=(b(n-1)*b(n-2)+(3+(-1)^n)/2)/b(n-3) then b(n)=abs(a(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 03 2007
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PROG
| Floretion Algebra Multiplication Program. FAMP code: em[J* ]sigcycseq[ + .75'i + .5'k + .25i' + .5j' + .5k' - .25'ii' + .25'jj' - .25'kk' - .75'jk' + .5'ki' - .25'kj' + .25e]
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CROSSREFS
| Elements of even index in the sequence gives A004253. Elements of odd index in the sequence gives A002310.
Cf. A004253, A002310.
Sequence in context: A192673 A193021 A112569 * A206301 A026776 A117160
Adjacent sequences: A101460 A101461 A101462 * A101464 A101465 A101466
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KEYWORD
| easy,sign
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AUTHOR
| Creighotn Dement (creighton.k.dement(AT)uni-oldenburg.de), Jan 20 2005
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