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A088981
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a(n+2) = a(n+1) + a(n) - [(2*n)+1] where a(0)=7, a(1)=11.
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1
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7, 11, 17, 25, 37, 55, 83, 127, 197, 309, 489, 779, 1247, 2003, 3225, 5201, 8397, 13567, 21931, 35463, 57357, 92781, 150097, 242835, 392887, 635675, 1028513, 1664137, 2692597, 4356679, 7049219, 11405839, 18454997
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OFFSET
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0,1
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REFERENCES
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J. Baylis and R. Haggarty, Alice in Numberland, A Student's Guide to the Enjoyment of Higher Mathematics, Macmillan Education 1988.
G. Buckwell, Mastering Mathematics, Palgrave Master Series, 2nd Ed. 1997.
R. P. C. Forman, Additional Mathematics Pure & Applied, Stanley Thornes, 1989.
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LINKS
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FORMULA
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a(n) = [(2*(alpha^(n+3))) - (2*(beta^(n+3))) + ((2*sqrt5)*n) + (3*sqrt5)] / (sqrt5) where alpha = (1 + sqrt5) / 2 and beta = (1 - sqrt5) / 2.
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MATHEMATICA
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LinearRecurrence[{3, -2, -1, 1}, {7, 11, 17, 25}, 40] (* Harvey P. Dale, Jun 08 2018 *)
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PROG
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(PARI) a=[7, 11]; for(n=2, 10, a=concat(a, a[#a]+a[#a-1]-2*n+3)); a
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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