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A051678 Square-pyramid-tree numbers: a(n) = sum(b(m),m=1..n), b(m) = 1^2, 1^2,2^2, 1^2,2^2,3^2,.. = (A002260)^2. 1

%I

%S 1,2,6,7,11,20,21,25,34,50,51,55,64,80,105,106,110,119,135,160,196,

%T 197,201,210,226,251,287,336,337,341,350,366,391,427,476,540,541,545,

%U 554,570,595,631,680,744,825,826,830,839,855,880,916,965,1029,1110,1210

%N Square-pyramid-tree numbers: a(n) = sum(b(m),m=1..n), b(m) = 1^2, 1^2,2^2, 1^2,2^2,3^2,.. = (A002260)^2.

%H Ivan Neretin, <a href="/A051678/b051678.txt">Table of n, a(n) for n = 1..5050</a>

%F a(n * (n + 1)/2 + m) = 1/12 * n * (n + 2) * (n + 1)^2 + 1/6 * m * (m + 1) * (2 * m + 1) = A002415(n) + A000330(m), m = 0...n + 1, n = 1, 2, 3..

%t Table[n^2 (n^2 - 1)/12 + m (m + 1) (2 m + 1)/6, {n, 10}, {m, n}] // Flatten (* _Ivan Neretin_, May 22 2015 *)

%Y Cf. A002260, A000330, A002415.

%K easy,nice,nonn

%O 1,2

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)

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Last modified March 30 06:59 EDT 2020. Contains 333119 sequences. (Running on oeis4.)