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A022415
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Kim-sums: "Kimberling sums" K_n + K_4.
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4
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3, 10, 13, 15, 18, 21, 23, 26, 28, 31, 34, 36, 39, 42, 44, 47, 49, 52, 55, 57, 60, 62, 65, 68, 70, 73, 76, 78, 81, 83, 86, 89, 91, 94, 97, 99, 102, 104, 107, 110, 112, 115, 117, 120, 123, 125, 128, 131, 133, 136, 138, 141, 144, 146, 149, 151, 154, 157, 159, 162, 165, 167, 170, 172, 175, 178
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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REFERENCES
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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..65.
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:
A022415 := proc(n)
if n = 0 then
3;
else
Kisum(n-1, 3) ;
end if;
end proc:
seq(A022415(n), n=0..80) ; # R. J. Mathar, Sep 03 2016
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CROSSREFS
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The "Kim-sums" K_n + K_i for i = 2 through 12 are given in A022413, A022414, A022415, A022416, ..., A022423.
Sequence in context: A358266 A299403 A174242 * A344619 A299983 A188373
Adjacent sequences: A022412 A022413 A022414 * A022416 A022417 A022418
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KEYWORD
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nonn
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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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