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Number of compositions (ordered partitions) of n into distinct square pyramidal numbers.
2

%I #6 Feb 16 2025 08:33:59

%S 1,1,0,0,0,1,2,0,0,0,0,0,0,0,1,2,0,0,0,2,6,0,0,0,0,0,0,0,0,0,1,2,0,0,

%T 0,2,6,0,0,0,0,0,0,0,2,6,0,0,0,6,24,0,0,0,0,1,2,0,0,0,2,6,0,0,0,0,0,0,

%U 0,2,6,0,0,0,6,24,0,0,0,0,0,0,0,0,0,2,6,0,0,0,6,25

%N Number of compositions (ordered partitions) of n into distinct square pyramidal numbers.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarePyramidalNumber.html">Square Pyramidal Number</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%e a(20) = 6 because we have [14, 5, 1], [14, 1, 5], [5, 14, 1], [5, 1, 14], [1, 14, 5] and [1, 5, 14].

%Y Cf. A000330, A279220, A298246, A322340, A331844, A331919.

%K nonn,changed

%O 0,7

%A _Ilya Gutkovskiy_, Feb 03 2020