cp's OEIS Frontend

A333516 Irregular triangle read by rows in which row n lists the first A000217(n) terms of A002260, n >= 1.

%I A333516 #54 Nov 10 2024 15:59:09
%S A333516 1,1,1,2,1,1,2,1,2,3,1,1,2,1,2,3,1,2,3,4,1,1,2,1,2,3,1,2,3,4,1,2,3,4,
%T A333516 5,1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6,1,1,2,1,2,3,1,2,3,4,1,2,
%U A333516 3,4,5,1,2,3,4,5,6,1,2,3,4,5,6,7,1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6
%N A333516 Irregular triangle read by rows in which row n lists the first A000217(n) terms of A002260, n >= 1.
%C A333516 a(n) equals the difference between n and the largest number less than n that can be expressed as the sum of the i-th triangular number and the j-th tetrahedral number for integers i < j.
%F A333516 a(n) = A002260(A124171(n)).
%e A333516 Triangle begins:
%e A333516   1;
%e A333516   1, 1, 2;
%e A333516   1, 1, 2, 1, 2, 3;
%e A333516   1, 1, 2, 1, 2, 3, 1, 2, 3, 4;
%e A333516   1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5;
%e A333516   1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6;
%e A333516   1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7;
%e A333516   ...
%p A333516 T:= n-> seq([$1..i][], i=1..n):
%p A333516 seq(T(n), n=1..7);  # _Alois P. Heinz_, Apr 10 2020
%o A333516 (Python)
%o A333516 from math import comb, isqrt
%o A333516 from sympy import integer_nthroot
%o A333516 def A333516(n): return (r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(n>comb(m+2,3))+1,3))-comb((k:=isqrt(m:=r+1<<1))+(m>k*(k+1)),2)+1 # _Chai Wah Wu_, Nov 10 2024
%Y A333516 Row sums give A000292.
%Y A333516 Right border gives A000027.
%Y A333516 Cf. A000217, A002260, A124171.
%K A333516 nonn,easy,tabf
%O A333516 1,4
%A A333516 _Andrew Slattery_, Mar 25 2020