A307357 Row sums of triangle A307116.

1, 2, 4, 8, 5, 10, 11, 10, 17, 22, 12, 24, 25, 18, 30, 36, 20, 40, 47, 24, 42, 42, 32, 46, 58, 34, 50, 58, 52, 60, 63, 50, 73, 64, 56, 84, 82, 56, 83, 88, 58, 86, 88, 74, 99, 96, 76, 106, 96, 90, 136, 124, 75, 108, 131, 82, 106, 142, 130, 132, 127, 104, 129

Offset: 0

Author

Rémy Sigrist, Apr 04 2019

Keywords

• nonn

Comments

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.

Examples

			The first terms, alongside the corresponding rows in A307116, are:
  n  a(n)  Row n of A307116
  -  ----  ----------------
  0     1           1
  1     2          1 1
  2     4         1 2 1
  3     8        1 3 3 1
  4     5       1 1 1 1 1
  5    10      1 2 2 2 2 1
  6    11     1 3 1 1 1 3 1
  7    10    1 1 1 2 2 1 1 1
  8    17   1 2 2 3 1 3 2 2 1
  9    22  1 3 1 5 1 1 5 1 3 1
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..25000
• Rémy Sigrist, Colored scatterplot of (n, a(n)) for n = 0..100000 (where the color is function of n mod 3)

Crossrefs

Cf. A307116.

Programs

PARI

fibs = Set(vector(100,k,fibonacci(k)))
f(s) = if (setsearch(fibs, s), s, 1)
{ 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) ", ")) }

Formula

a(n) = Sum_{k = 0..n} A307116(n, k).