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A363284 Numbers that are square or square pyramidal.

%I A363284 #20 Aug 04 2023 04:58:20
%S A363284 0,1,4,5,9,14,16,25,30,36,49,55,64,81,91,100,121,140,144,169,196,204,
%T A363284 225,256,285,289,324,361,385,400,441,484,506,529,576,625,650,676,729,
%U A363284 784,819,841,900,961,1015,1024,1089,1156,1225,1240,1296,1369,1444,1496
%N A363284 Numbers that are square or square pyramidal.
%C A363284 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.
%C A363284 4900 is the only nontrivial case of a square number that is also square pyramidal (proved by Watson). - _Peter Munn_, Jul 30 2023
%D A363284 W. Ljunggren, New solution of a problem proposed by E. Lucas, Norsk Mat. Tidsskr. 34 (1952), pp 65-72.
%D A363284 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, 1987, entry 24, p 101.
%H A363284 Michael A. Bennett, <a href="http://www.math.ubc.ca/~bennett/paper21.pdf">Lucas' Square Pyramid Problem Revisited</a>.
%H A363284 E. Lucas, <a href="http://www.numdam.org/item/NAM_1875_2_14__336_0/">Problem 1180</a>, Nouvelles Ann. Math. (2) 14 (1875), p 336.
%H A363284 G. N. Watson, <a href="http://archive.org/stream/messengerofmathe4849cambuoft#page/n9/mode/2up">The problem of the square pyramid</a>, Messenger of Mathematics 48 (1918), pp. 1-22.
%t A363284 c[1] = 1; c[2] = 1;
%t A363284 c[n_] := If[OddQ[n], c[n - 2] + n, c[n - 2] + c[n - 1]]
%t A363284 u = Table[c[n], {n, 1, 120}]  (* A363269 *)
%t A363284 FindLinearRecurrence[u]
%t A363284 Union[u] (* this sequence *)
%Y A363284 Cf. A000290, A000330, A363269.
%K A363284 nonn
%O A363284 1,3
%A A363284 _Clark Kimberling_, May 25 2023
%E A363284 Name simplified and 0 prefixed to data by _Peter Munn_, Jul 30 2023