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A166863
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a(1)= 1; a(2)= 5; thereafter a(n)= a(n-1) + a(n-2) + 5.
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5
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1, 5, 11, 21, 37, 63, 105, 173, 283, 461, 749, 1215, 1969, 3189, 5163, 8357, 13525, 21887, 35417, 57309, 92731, 150045, 242781, 392831, 635617, 1028453, 1664075, 2692533, 4356613, 7049151, 11405769, 18454925, 29860699, 48315629, 78176333, 126491967
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - a(n-3).
G.f: x*(1+3*x+x^2)/((x-1)* (x^2+x-1)). (End)
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EXAMPLE
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a(3) = 5 + 1 + 5 = 11.
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MATHEMATICA
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RecurrenceTable[{a[1]==1, a[2]==5, a[n]==a[n-1]+a[n-2]+5}, a, {n, 40}] (* or *) LinearRecurrence[{2, 0, -1}, {1, 5, 11}, 40] (* Harvey P. Dale, Jan 29 2021 *)
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PROG
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(Haskell)
a166863 n = a166863_list !! (n-1)
a166863_list = 1 : zipWith (+) a166863_list (drop 3 $ map (* 2) a000045_list)
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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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EXTENSIONS
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STATUS
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approved
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