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

0,2

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.

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)

Formula

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

Example

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

Prog

(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) ", ")) }

Crossrefs

Cf. A307116.

Sequence in context: A300890 A021893 A036117 * A116624 A366304 A361191

Adjacent sequences: A307354 A307355 A307356 * A307358 A307359 A307360

Keyword

nonn

Author

Rémy Sigrist, Apr 04 2019

Status

approved