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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
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
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