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A307357 Row sums of triangle A307116.

%I A307357 #10 Apr 05 2019 12:39:44
%S A307357 1,2,4,8,5,10,11,10,17,22,12,24,25,18,30,36,20,40,47,24,42,42,32,46,
%T A307357 58,34,50,58,52,60,63,50,73,64,56,84,82,56,83,88,58,86,88,74,99,96,76,
%U A307357 106,96,90,136,124,75,108,131,82,106,142,130,132,127,104,129
%N A307357 Row sums of triangle A307116.
%C A307357 The scatterplot of the sequence shows 3 beams of points; this could be related to the regular structure visible on both sides of the triangle A307116.
%H A307357 Rémy Sigrist, <a href="/A307357/b307357.txt">Table of n, a(n) for n = 0..25000</a>
%H A307357 Rémy Sigrist, <a href="/A307357/a307357.png">Colored scatterplot of (n, a(n)) for n = 0..100000</a> (where the color is function of n mod 3)
%F A307357 a(n) = Sum_{k = 0..n} A307116(n, k).
%e A307357 The first terms, alongside the corresponding rows in A307116, are:
%e A307357   n  a(n)  Row n of A307116
%e A307357   -  ----  ----------------
%e A307357   0     1           1
%e A307357   1     2          1 1
%e A307357   2     4         1 2 1
%e A307357   3     8        1 3 3 1
%e A307357   4     5       1 1 1 1 1
%e A307357   5    10      1 2 2 2 2 1
%e A307357   6    11     1 3 1 1 1 3 1
%e A307357   7    10    1 1 1 2 2 1 1 1
%e A307357   8    17   1 2 2 3 1 3 2 2 1
%e A307357   9    22  1 3 1 5 1 1 5 1 3 1
%o A307357 (PARI) fibs = Set(vector(100,k,fibonacci(k)))
%o A307357 f(s) = if (setsearch(fibs, s), s, 1)
%o A307357 { for (r=0, 62, row = vector(r+1, k, if (k==1||k==r+1, 1, f(row[k-1]+row[k]))); print1 (vecsum(row) ", ")) }
%Y A307357 Cf. A307116.
%K A307357 nonn
%O A307357 0,2
%A A307357 _Rémy Sigrist_, Apr 04 2019