cp's OEIS Frontend

A376181 Array read by antidiagonals: Start from 1 and thereafter add gnomons of terms for each t >= 2 with width a(t-1).

%I A376181 #52 Feb 19 2025 12:12:11
%S A376181 1,2,2,3,2,3,3,3,3,3,4,3,3,3,4,4,4,3,3,4,4,5,4,4,3,4,4,5,5,5,4,4,4,4,
%T A376181 5,5,5,5,5,4,4,4,5,5,5,6,5,5,5,4,4,5,5,5,6,6,6,5,5,5,4,5,5,5,6,6,7,6,
%U A376181 6,5,5,5,5,5,5,6,6,7,7,7,6,6,5,5,5,5,5,6,6,7,7,7,7,7,6,6,5,5,5,5
%N A376181 Array read by antidiagonals: Start from 1 and thereafter add gnomons of terms for each t >= 2 with width a(t-1).
%C A376181 A gnomon is an L-shaped group of terms that are equal to each other and surrounds the top-left corner.
%C A376181 The sequence seems to oscillate a lot and it seems that log(a(n))/log(n) doesn't converge. However, log(max{a(i); i < n})/log(n) appears to converge to around ~0.387.
%C A376181 The formula a(d(d+1)/2) = n, where d = 1 + (a(1) + ... + a(n-1)), suggests that the sequence might be growing like k*n^c on average, where c = (sqrt(3)-1)/2.
%C A376181 The construction is similar to the Golomb sequence (A001462) in that sequence terms themselves determine repetitions, but here those repetitions are gnomon widths.
%F A376181 a(d(d+1)/2) = n, where d = 1 + (a(1) + ... + a(n-1)), for n > 1.
%F A376181 a(n) ~ k*n^c, on average, where c = (sqrt(3)-1)/2 = 0.366... (heuristic).
%F A376181 max{a(i); i < n} ~ K*n^e with e ~ 0.387...  (empirical).
%e A376181 Array begins:
%e A376181       k=1 2 3 4 5 6
%e A376181   n=1:  1 2 3 3 4 4
%e A376181   n=2:  2 2 3 3 4 4
%e A376181   n=3:  3 3 3 3 4 4
%e A376181   n=4:  3 3 3 3 4 4
%e A376181   n=5:  4 4 4 4 4 4
%e A376181   n=6:  4 4 4 4 4 4
%e A376181 The first three terms by antidiagonals are 1,2,2 and they are the widths of the gnomons comprising terms 2,3,4 respectively.
%Y A376181 Cf. A001462, A283683.
%K A376181 nonn,tabl
%O A376181 1,2
%A A376181 _Bryle Morga_, Sep 14 2024