

A363284


Numbers that are square or square pyramidal.


2



0, 1, 4, 5, 9, 14, 16, 25, 30, 36, 49, 55, 64, 81, 91, 100, 121, 140, 144, 169, 196, 204, 225, 256, 285, 289, 324, 361, 385, 400, 441, 484, 506, 529, 576, 625, 650, 676, 729, 784, 819, 841, 900, 961, 1015, 1024, 1089, 1156, 1225, 1240, 1296, 1369, 1444, 1496
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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 6572.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, 1987, entry 24, p 101.


LINKS

E. Lucas, Problem 1180, Nouvelles Ann. Math. (2) 14 (1875), p 336.


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



EXTENSIONS

Name simplified and 0 prefixed to data by Peter Munn, Jul 30 2023


STATUS

approved



