

A226141


Sum of the squared parts of the partitions of n into exactly two parts.


2



0, 2, 5, 18, 30, 64, 91, 156, 204, 310, 385, 542, 650, 868, 1015, 1304, 1496, 1866, 2109, 2570, 2870, 3432, 3795, 4468, 4900, 5694, 6201, 7126, 7714, 8780, 9455, 10672, 11440, 12818, 13685, 15234, 16206, 17936, 19019, 20940, 22140, 24262, 25585, 27918, 29370, 31924, 33511
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OFFSET

1,2


LINKS



FORMULA

a(n) = Sum_{i=1..floor(n/2)} (i^2 + (ni)^2).
a(n) = ((n/2)^2) * (1  ceiling(n/2) + floor(n/2)) + Sum_{i=1..n1} i^2.
a(n) = n*(8*n^2  9*n + 4)/24 + (1)^n*n^2/8.  Giovanni Resta, May 29 2013
G.f.: x^2*(2+3*x+7*x^2+3*x^3+x^4) / ( (1+x)^3*(x1)^4 ).  R. J. Mathar, Jun 07 2013


EXAMPLE

a(5) = 30; 5 has exactly 2 partitions into two parts, (4,1) and (3,2). Squaring the parts and adding, we get: 1^2 + 2^2 + 3^2 + 4^2 = 30.


MAPLE

a:=n>sum(i^2 + (ni)^2, i=1..floor(n/2)); seq((a(k), k=1..40);


MATHEMATICA

LinearRecurrence[{1, 3, 3, 3, 3, 1, 1}, {0, 2, 5, 18, 30, 64, 91}, 50] (* Harvey P. Dale, Jul 23 2019 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



