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A294139 Sum of the areas of the distinct rectangles (and the areas of the squares on their sides) with positive integer sides such that L + W = n, W < L. 0
0, 0, 12, 23, 70, 105, 210, 282, 468, 590, 880, 1065, 1482, 1743, 2310, 2660, 3400, 3852, 4788, 5355, 6510, 7205, 8602, 9438, 11100, 12090, 14040, 15197, 17458, 18795, 21390, 22920, 25872, 27608, 30940, 32895, 36630, 38817, 42978, 45410, 50020, 52710, 57792 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..43.

FORMULA

a(n) = Sum_{i=1..floor((n-1)/2)} 2*i^2 + 2*(n-i)^2 + i*(n-i).

Conjectures from Colin Barker, Nov 01 2017: (Start)

G.f.: x^3*(12 + 11*x + 11*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3).

a(n) = n*(6*n - 1)*(n - 2) / 8 for n even.

a(n) = n*(3*n - 1)*(n - 1) / 4 for n odd.

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n > 7.

(End)

MATHEMATICA

Table[ Sum[2 i^2 + 2 (n - i)^2 + i (n - i), {i, Floor[(n-1)/2]}], {n, 40}]

CROSSREFS

Cf. A294473.

Sequence in context: A190426 A207539 A083683 * A255766 A015447 A072822

Adjacent sequences:  A294136 A294137 A294138 * A294140 A294141 A294142

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Oct 31 2017

STATUS

approved

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Last modified March 20 05:34 EDT 2019. Contains 321344 sequences. (Running on oeis4.)