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A120165
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a(n) = 7 + floor((1 + Sum_{j=1..n-1} a(j))/4).
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2
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7, 9, 11, 14, 17, 21, 27, 33, 42, 52, 65, 81, 102, 127, 159, 199, 248, 310, 388, 485, 606, 758, 947, 1184, 1480, 1850, 2312, 2890, 3613, 4516, 5645, 7056, 8820, 11025, 13782, 17227, 21534, 26917, 33647, 42058
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) ~ c (5/4)^n with c approximately 5.5905081519. - Robert Israel, Mar 20 2017
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MAPLE
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A[1]:= 7: S:= 7:
for n from 2 to 100 do A[n]:= floor((29 + S)/4); S:= S + A[n] od:
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MATHEMATICA
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a = {7}; Do[AppendTo[a, Floor[(29 + Total@ a)/4]], {i, 2, 40}]; a (* Michael De Vlieger, Mar 20 2017 *)
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PROG
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(Magma)
function f(n, a, b)
t:=0;
for k in [1..n-1] do
t+:= a+Floor((b+t)/4);
end for;
return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
(SageMath)
@CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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