This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A070770 #21 Dec 11 2024 15:42:29 %S A070770 0,1,2,3,2,3,4,4,5,6,3,4,5,5,6,7,6,7,8,9,4,5,6,6,7,8,7,8,9,10,8,9,10, %T A070770 11,12,5,6,7,7,8,9,8,9,10,11,9,10,11,12,13,10,11,12,13,14,15,6,7,8,8, %U A070770 9,10,9,10,11,12,10,11,12,13,14,11,12,13,14,15,16,12,13,14,15,16,17,18,7 %N A070770 b + c + d where b >= c >= d >= 0 ordered by b then c then d. %H A070770 Robert Israel, <a href="/A070770/b070770.txt">Table of n, a(n) for n = 0..10000</a> %F A070770 a(n) = A056556(n) + A056557(n) + A056558(n). %e A070770 Triangle begins: %e A070770 0, %e A070770 ; %e A070770 1; %e A070770 2, 3; %e A070770 ; %e A070770 2; %e A070770 3, 4; %e A070770 4, 5, 6; %e A070770 ; %e A070770 3; %e A070770 4, 5, %e A070770 5, 6, 7; %e A070770 6, 7, 8, 9; %e A070770 ; %e A070770 4; %e A070770 5, 6; %e A070770 6, 7, 8; %e A070770 7, 8, 9, 10; %e A070770 8, 9, 10, 11, 12; %e A070770 ; %e A070770 ... %p A070770 seq(seq(seq(b+c+d,d=0..c),c=0..b),b=0..10); # _Robert Israel_, Jun 21 2018 %o A070770 (PARI) for(x=0,5,for(y=0,x,for(z=0,y,print1(x+y+z", ")))) \\ _Charles R Greathouse IV_, Sep 17 2015 %o A070770 (Python) %o A070770 from math import isqrt, comb %o A070770 from sympy import integer_nthroot %o A070770 def A070770(n): return (m:=integer_nthroot(6*(n+1),3)[0])+(a:=n>=comb(m+2,3))+(k:=isqrt(b:=(c:=n+1-comb(m+a+1,3))<<1))-((b<<2)<=(k<<2)*(k+1)+1)+c-2-comb(k+(b>k*(k+1)),2) # _Chai Wah Wu_, Dec 11 2024 %Y A070770 Cf. A001477, A051162, A070771, A070772 for similar sequences with different numbers of terms summed. %K A070770 nonn,look,tabf %O A070770 0,3 %A A070770 _Henry Bottomley_, May 06 2002