OFFSET
1,3
COMMENTS
This sequence essentially consists of the numbers in A363269 arranged in increasing order. Although A363269 is a linear recurrence sequence, it appears that this sequence is not.
4900 is the only nontrivial case of a square number that is also square pyramidal (proved by Watson). - Peter Munn, Jul 30 2023
REFERENCES
W. Ljunggren, New solution of a problem proposed by E. Lucas, Norsk Mat. Tidsskr. 34 (1952), pp 65-72.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, 1987, entry 24, p 101.
LINKS
Michael A. Bennett, Lucas' Square Pyramid Problem Revisited.
E. Lucas, Problem 1180, Nouvelles Ann. Math. (2) 14 (1875), p 336.
G. N. Watson, The problem of the square pyramid, Messenger of Mathematics 48 (1918), pp. 1-22.
MATHEMATICA
c[1] = 1; c[2] = 1;
c[n_] := If[OddQ[n], c[n - 2] + n, c[n - 2] + c[n - 1]]
u = Table[c[n], {n, 1, 120}] (* A363269 *)
FindLinearRecurrence[u]
Union[u] (* this sequence *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 25 2023
EXTENSIONS
Name simplified and 0 prefixed to data by Peter Munn, Jul 30 2023
STATUS
approved