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A014369 a(n) = bcd, where n = C(b,3)+C(c,2)+C(d,1), b>c>d>=0.

%I A014369 #16 Jul 08 2025 05:37:51
%S A014369 310,320,321,410,420,421,430,431,432,510,520,521,530,531,532,540,541,
%T A014369 542,543,610,620,621,630,631,632,640,641,642,643,650,651,652,653,654,
%U A014369 710,720,721,730,731,732,740,741,742,743,750,751,752,753
%N A014369 a(n) = bcd, where n = C(b,3)+C(c,2)+C(d,1), b>c>d>=0.
%C A014369 In the definition bcd means concatenation not multiplication. - _Sean A. Irvine_, Oct 18 2018
%D A014369 W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge, 1993, p. 158.
%p A014369 invA000292 := proc(n)
%p A014369     local i;
%p A014369     for i from 1 do
%p A014369         if binomial(i+1,3) > n then
%p A014369             return i;
%p A014369         end if;
%p A014369     end do:
%p A014369 end proc:
%p A014369 invA000217 := proc(n)
%p A014369     local i;
%p A014369     for i from 1 do
%p A014369         if binomial(i+1,2) > n then
%p A014369             return i;
%p A014369         end if;
%p A014369     end do:
%p A014369 end proc:
%p A014369 A014369 := proc(n)
%p A014369     local b,c,d ;
%p A014369     b := invA000292(n) ;
%p A014369     c := invA000217(n-binomial(b,3)) ;
%p A014369     d := n-binomial(b,3)-binomial(c,2) ;
%p A014369     digcatL([b,c,d]) ; # of program transforms
%p A014369 end proc:
%p A014369 seq(A014369(n),n=1..70) ; # _R. J. Mathar_, May 25 2023
%K A014369 nonn,easy
%O A014369 1,1
%A A014369 _N. J. A. Sloane_
%E A014369 a(1), a(4), a(10), a(20), a(35) modified to meet constraint b>c>d and more terms from _Sean A. Irvine_, Oct 18 2018