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A023537
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Lucas(n+4) - (3n+7).
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10
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1, 5, 13, 28, 54, 98, 171, 291, 487, 806, 1324, 2164, 3525, 5729, 9297, 15072, 24418, 39542, 64015, 103615, 167691, 271370, 439128, 710568, 1149769, 1860413, 3010261, 4870756, 7881102, 12751946, 20633139, 33385179, 54018415, 87403694, 141422212
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| W. Lang in: "Applications of Fibonacci Numbers", Vol. 7, p. 235, eds.: G. E. Bergum et al., Kluwer, 1998.
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FORMULA
| Convolution of natural numbers with Lucas numbers A000204.
a(n)=7*(F(n+1)-1)+4*F(n)-3*n; F(n)= A000045 (Fibonacci), G.F. x*(1+2*x)/((1-x-x^2)*(1-x)^2) -from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de).
a(n) - a(n-1) = A101220(3,1,n). - Ross La Haye (rlahaye(AT)new.rr.com), May 31 2006
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MAPLE
| with(combinat): L:=n->fibonacci(n+2)-fibonacci(n-2): seq(L(n), n=0..12): seq(L(n+4)-3*n-7, n=1..40); (Deutsch)
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PROG
| (MAGMA) [Lucas(n+4) - (3*n+7): n in [1..100]]; // Vincenzo Librandi, Apr 16 2011
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CROSSREFS
| T(n, n+2), T given by A027960.
Sequence in context: A175254 A055328 A027962 * A023653 A060182 A147066
Adjacent sequences: A023534 A023535 A023536 * A023538 A023539 A023540
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KEYWORD
| nonn,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 08 2005
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