A341474 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)^2 + t(1)^2 + t(2)^2 for an element t of T containing n.

0, 1, 1, 1, 1, 2, 1, 1, 4, 3, 2, 1, 4, 1, 4, 5, 5, 3, 2, 5, 1, 6, 4, 6, 1, 5, 4, 5, 9, 5, 9, 3, 10, 2, 10, 5, 8, 1, 6, 9, 4, 17, 6, 13, 1, 11, 5, 13, 4, 9, 5, 9, 16, 5, 18, 9, 14, 3, 14, 10, 9, 2, 12, 10, 5, 21, 8, 19, 1, 17, 6, 19, 9, 10, 4, 17, 17, 6, 26, 13

Offset

0,6

Comments

This sequence is a variant of A286327; here we consider tribonacci-like sequences, there Fibonacci like sequences. The scatterplots of these sequences are similar.

Links

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

Rémy Sigrist, Scatterplot of the first 100000 terms

Rémy Sigrist, Scatterplot of the first 1000000 terms

Rémy Sigrist, PARI program for A341474

Formula

a(n) = 0 iff n = 0.

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

a(n) <= n^2.

Example

The first terms of the elements t of T such that t(0)^2 + t(1)^2 + t(2)^2 <= 4 are:
  t(0)^2+t(1)^2+t(3)^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     1     1     2     4     7    13    24    44    81
                     2     1     0     1     2     3     6    11    20    37    68
                     2     1     1     0     2     3     5    10    18    33    61
                     3     1     1     1     3     5     9    17    31    57   105
                     4     0     0     2     2     4     8    14    26    48    88
                     4     0     2     0     2     4     6    12    22    40    74
                     4     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(10) = a(18) = 2,
     a(9) = a(17) = 3,
     a(8) = a(12) = a(14) = 4.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000073, A001590, A213816, A286327, A341456.

Sequence in context: A306790 A332056 A074744 * A339303 A369588 A010360

Adjacent sequences: A341471 A341472 A341473 * A341475 A341476 A341477

Keyword

nonn,look

Author

Rémy Sigrist, Feb 13 2021

Status

approved