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A022414
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Kim-sums: "Kimberling sums" K_n + K_3.
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4
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2, 7, 10, 4, 15, 18, 20, 23, 9, 28, 31, 12, 36, 39, 41, 44, 17, 49, 52, 54, 57, 22, 62, 65, 25, 70, 73, 75, 78, 30, 83, 86, 33, 91, 94, 96, 99, 38, 104, 107, 109, 112, 43, 117, 120, 46, 125, 128, 130, 133, 51, 138, 141, 143, 146, 56, 151, 154, 59, 159, 162, 164, 167
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OFFSET
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0,1
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COMMENTS
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Let W(i,j) denote the index of that row of the extended Wythoff array (see A035513) that contains the sequence formed by the sum of rows i and j. Then a(n) = W(2,n). - N. J. A. Sloane, Mar 07 2016
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REFERENCES
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J. H. Conway, Posting to Math Fun Mailing List, Dec 02 1996.
M. LeBrun, Posting to Math Fun Mailing List Jan 10 1997.
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LINKS
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Table of n, a(n) for n=0..62.
J. H. Conway, Allan Wechsler, Marc LeBrun, Dan Hoey, N. J. A. Sloane, On Kimberling Sums and Para-Fibonacci Sequences, Correspondence and Postings to Math-Fun Mailing List, Nov 1996 to Jan 1997
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MAPLE
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Ki := proc(n, i)
option remember;
local phi ;
phi := (1+sqrt(5))/2 ;
if i= 0 then
n;
elif i=1 then
floor((n+1)*phi) ;
else
procname(n, i-1)+procname(n, i-2) ;
end if;
end proc:
Kisum := proc(n, m)
local ks, a, i;
ks := [seq( Ki(n, i)+Ki(m, i), i=0..5)] ;
for i from 0 to 2 do
for a from 0 do
if Ki(a, 0) = ks[i+1] and Ki(a, 1) = ks[i+2] then
return a;
end if;
if Ki(a, 0) > ks[i+1] then
break;
end if;
end do:
end do:
end proc:
A022414 := proc(n)
if n = 0 then
2;
else
Kisum(n-1, 2) ;
end if;
end proc:
seq(A022414(i), i=0..80) ; # R. J. Mathar, Sep 03 2016
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CROSSREFS
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Cf. A000201, A035513.
The "Kim-sums" K_n + K_i for i = 2 through 12 are given in A022413, A022414, A022415, A022416, ..., A022423.
Sequence in context: A041453 A042157 A012937 * A319932 A236243 A024831
Adjacent sequences: A022411 A022412 A022413 * A022415 A022416 A022417
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KEYWORD
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nonn,easy
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AUTHOR
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Marc LeBrun
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STATUS
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approved
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