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Number of partitions of n into two distinct arithmetic numbers.
1

%I #4 Feb 05 2024 13:04:39

%S 0,0,0,1,0,1,1,2,1,1,1,2,1,2,1,3,2,4,2,5,3,4,3,5,4,5,4,6,3,5,3,6,5,8,

%T 5,9,5,7,4,8,6,9,7,11,7,9,7,11,9,13,8,14,8,11,8,13,11,14,11,16,12,15,

%U 11,15,12,16,13,18,12,15,14,18,16,19,15,20,14,16,15

%N Number of partitions of n into two distinct arithmetic numbers.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{k=1..floor((n-1)/2)} c(k) * c(n-k), where c = A245656.

%e a(14) = 2 ways (13+1 = 11+3, we do not count 7+7).

%t a[n_] := Boole[IntegerQ[Mean[Divisors[n]]]]; Table[Sum[a[k]*a[n - k], {k, Floor[(n - 1)/2]}], {n, 100}]

%Y Cf. A003601, A245656, A369916.

%K nonn,easy

%O 1,8

%A _Wesley Ivan Hurt_, Feb 05 2024