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A309167 a(n)^2 is the least possible value at the root of a binary tree of height n where all nodes hold positive squares and all interior nodes also equal the sum of their two children. 2
1, 5, 13, 65, 97, 229, 997, 1145, 2245, 5725, 7213, 9805, 10445, 24193, 34121, 37321, 52225, 83729, 98449, 125233, 145493, 156925, 171037, 260893, 334981, 345725, 457813, 576757 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We have binary trees with the desired properties for every height n > 0:

- for n = 1: we have the following tree B_1:

                     1^2

                      |

- for any n > 0, provided we have B_n, we can build a tree B_{n+1) as follows:

              3^2*B_n   4^2*B_n

                  \       /

                   \     /

                    \   /

                   (5^n)^2

                      |

- hence the sequence is well defined.

LINKS

Table of n, a(n) for n=1..28.

Rémy Sigrist, Illustration of first terms

Rémy Sigrist, C++ program for A309167

FORMULA

a(n) <= 5^(n-1).

A309228(a(n)) = n and A309228(k) < n for any k < a(n).

EXAMPLE

a(1) = 1:

              1^2

               |

a(2) = 5:

           3^2    4^2

            \     /

             \   /

              5^2

               |

a(3) = 13:

          3^2    4^2

           \     /

            \   /

             5^2    12^2

              \      /

               \    /

                13^2

                  |

PROG

(C++) See Links section.

CROSSREFS

Cf. A000351, A309228.

Sequence in context: A149573 A149574 A301634 * A272069 A018678 A149575

Adjacent sequences:  A309164 A309165 A309166 * A309168 A309169 A309170

KEYWORD

nonn,more

AUTHOR

Rémy Sigrist, Jul 15 2019

STATUS

approved

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Last modified December 9 09:21 EST 2019. Contains 329877 sequences. (Running on oeis4.)