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%I #10 Jun 09 2023 05:09:06
%S 4,13,16,18,21,24,26,29,31,34,37,39,42,45,47,50,52,55,58,60,63,65,68,
%T 71,73,76,79,81,84,86,89,92,94,97,100,102,105,107,110,113,115,118,120,
%U 123,126,128,131,134,136,139,141,144,147,149,152,154,157,160,162,165,168,170
%N Kim-sums: "Kimberling sums" K_n + K_5.
%D Posting to math-fun mailing list Jan 10 1997.
%p Ki := proc(n,i)
%p option remember;
%p local phi ;
%p phi := (1+sqrt(5))/2 ;
%p if i= 0 then
%p n;
%p elif i=1 then
%p floor((n+1)*phi) ;
%p else
%p procname(n,i-1)+procname(n,i-2) ;
%p end if;
%p end proc:
%p Kisum := proc(n,m)
%p local ks,a,i;
%p ks := [seq( Ki(n,i)+Ki(m,i),i=0..5)] ;
%p for i from 0 to 2 do
%p for a from 0 do
%p if Ki(a,0) = ks[i+1] and Ki(a,1) = ks[i+2] then
%p return a;
%p end if;
%p if Ki(a,0) > ks[i+1] then
%p break;
%p end if;
%p end do:
%p end do:
%p end proc:
%p A022416 := proc(n)
%p if n = 0 then
%p 4;
%p else
%p Kisum(n-1,4) ;
%p end if;
%p end proc:
%p seq(A022416(n),n=0..80) ; # _R. J. Mathar_, Sep 03 2016
%t 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]];
%t 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[]]]]];
%t A022416[n_] := If[n == 0, 4, Kisum[n-1, 4]];
%t Table[A022416[n], {n, 0, 80}] (* _Jean-François Alcover_, Jun 09 2023, after _R. J. Mathar_ *)
%K nonn
%O 0,1
%A _Marc LeBrun_
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