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A033818
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Convolution of natural numbers n >= 1 with Lucas numbers L(k) for k >= -2.
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0
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3, 5, 9, 14, 22, 34, 53, 83, 131, 208, 332, 532, 855, 1377, 2221, 3586, 5794, 9366, 15145, 24495, 39623, 64100, 103704, 167784, 271467, 439229, 710673, 1149878, 1860526, 3010378
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| a(n) = L(1)*(F(n+1)-1)+L(0)*F(n)-L(-1)*n, F(n): Fibonacci (A000045), L(n): Lucas (A000032) with L(-n)=(-1)^n*L(n)
G.F. x*(3-4*x)/((1-x-x^2)*(1-x)^2), 3=L(-2), -4=+L(-3).
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MATHEMATICA
| Abs[Join[{a=0, b=0}, Table[c=1*b+1*a+n; a=b; b=c, {n, -3, 60}]]] (*From Vladimir Joseph Stephan Orlovsky, Jan 28 2011*)
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CROSSREFS
| Cf. A023548, A023537, A033811.
Sequence in context: A166709 A053618 A032801 * A120452 A144116 A061556
Adjacent sequences: A033815 A033816 A033817 * A033819 A033820 A033821
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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