A341456 Let T be the set of sequences {t(k), k >= 0} such that for any k >= 3, t(k) = t(k-1) + t(k-2) + t(k-3); a(n) is the least possible value of t(0) + t(1) + t(2) for an element t of T containing n.

0, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 2, 1, 2, 3, 3, 3, 2, 3, 1, 3, 2, 4, 1, 3, 2, 3, 4, 3, 5, 3, 4, 2, 4, 3, 4, 1, 4, 3, 2, 5, 4, 5, 1, 5, 3, 5, 2, 5, 3, 5, 4, 3, 6, 5, 6, 3, 6, 4, 3, 2, 6, 4, 3, 5, 4, 7, 1, 7, 4, 7, 3, 4, 2, 7, 5, 4, 6, 5, 4, 1, 8, 5, 4, 3, 5

Offset

0,6

Comments

This sequence is a variant of A249783; here we consider tribonacci-like sequences, there Fibonacci like sequences. The scatterplots of these sequences both present polygonal shapes emerging from the origin.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, Scatterplot of the first 10000000 terms

Rémy Sigrist, PARI program for A341456

Formula

a(n) = 0 iff n = 0.

a(n) = 1 iff n belongs to A213816.

a(n) <= n.

Example

The first terms of the elements t of T such that t(0) + t(1) + t(2) <= 2 are:
  t(0)+t(1)+t(2)  t(0)  t(1)  t(2)  t(3)  t(4)  t(5)  t(6)  t(7)  t(8)  t(9)
  --------------  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----
               0     0     0     0     0     0     0     0     0     0     0
               1     0     0     1     1     2     4     7    13    24    44
               1     0     1     0     1     2     3     6    11    20    37
               1     1     0     0     1     1     2     4     7    13    24
               2     0     0     2     2     4     8    14    26    48    88
               2     0     1     1     2     4     7    13    24    44    81
               2     0     2     0     2     4     6    12    22    40    74
               2     1     0     1     2     3     6    11    20    37    68
               2     1     1     0     2     3     5    10    18    33    61
               2     2     0     0     2     2     4     8    14    26    48
- so a(0) = 0,
     a(1) = a(2) = a(3) = a(4) = a(6) = a(7) = a(11) = 1,
     a(5) = = a(8) = a(10) = 2.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000073, A001590, A213816, A249783.

Sequence in context: A255616 A014600 A165475 * A319420 A267134 A098280

Adjacent sequences: A341453 A341454 A341455 * A341457 A341458 A341459

Keyword

nonn

Author

Rémy Sigrist, Feb 12 2021

Status

approved