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Search: id:A001254
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| A001254 |
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Squares of Lucas numbers. |
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+0
9
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| 4, 1, 9, 16, 49, 121, 324, 841, 2209, 5776, 15129, 39601, 103684, 271441, 710649, 1860496, 4870849, 12752041, 33385284, 87403801, 228826129, 599074576, 1568397609, 4106118241, 10749957124, 28143753121, 73681302249
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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Thomas Koshy, "Fibonacci and Lucas Numbers and Applications", Wiley, New York, 2001.
A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 36,60.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
Tanya Khovanova, Recursive Sequences
T. Mansour, A note on sum of k-th power of Horadam's sequence
P. Stanica, Generating functions, weighted and non-weighted sums of powers...
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FORMULA
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G.f.: g(x)=(4-7x-x^2)/(1-2x-2x^2+x^3). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 30 2001
a(n)=r^n+(1/r)^n+2*(-1)^n, with r=(3+sqrt(5))/2. a(n+3)=2*a(n+2)+2*a(n+1)-a(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 08 2003
a(n) = L(2n) + 2(-1)^n = L(n-1)*L(n+1) + 5(-1)^n.
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CROSSREFS
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Cf. A000032, A000204.
Cf. A007598, A079291.
With alternating signs, cf. A075150.
Bisection of A001638 and A006499. First differences of A005970.
Second row of array A103324.
Adjacent sequences: A001251 A001252 A001253 this_sequence A001255 A001256 A001257
Sequence in context: A067015 A091885 A069606 this_sequence A075150 A128626 A028941
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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