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A022416
Kim-sums: "Kimberling sums" K_n + K_5.
4
4, 13, 16, 18, 21, 24, 26, 29, 31, 34, 37, 39, 42, 45, 47, 50, 52, 55, 58, 60, 63, 65, 68, 71, 73, 76, 79, 81, 84, 86, 89, 92, 94, 97, 100, 102, 105, 107, 110, 113, 115, 118, 120, 123, 126, 128, 131, 134, 136, 139, 141, 144, 147, 149, 152, 154, 157, 160, 162, 165, 168, 170
OFFSET
0,1
REFERENCES
Posting to math-fun mailing list Jan 10 1997.
MAPLE
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:
A022416 := proc(n)
if n = 0 then
4;
else
Kisum(n-1, 4) ;
end if;
end proc:
seq(A022416(n), n=0..80) ; # R. J. Mathar, Sep 03 2016
MATHEMATICA
Ki[n_, i_] := Ki[n, i] = Which[i == 0, n, i == 1, Floor[(n+1)* GoldenRatio], True, Ki[n, i-1] + Ki[n, i-2]];
Kisum[n_, m_] := Module[{ks, a, i}, ks = Table[Ki[n, i] + Ki[m, i], {i, 0, 5}]; For[i = 0, i <= 2, i++, For[a = 0, True, a++, If[Ki[a, 0] == ks[[i+1]] && Ki[a, 1] == ks[[i+2]], Return[a]]; If[Ki[a, 0] > ks[[i+1]], Break[]]]]];
A022416[n_] := If[n == 0, 4, Kisum[n-1, 4]];
Table[A022416[n], {n, 0, 80}] (* Jean-François Alcover, Jun 09 2023, after R. J. Mathar *)
CROSSREFS
Sequence in context: A126908 A106681 A144947 * A027757 A287361 A165336
KEYWORD
nonn
AUTHOR
STATUS
approved