A345026 Total area of all i X j rectangles where i and j are the final digits of positive integers r and s such that r + s = n.

0, 1, 2, 7, 10, 22, 28, 50, 60, 95, 100, 131, 122, 152, 130, 162, 128, 165, 120, 165, 200, 226, 242, 252, 250, 247, 228, 215, 180, 260, 300, 356, 362, 397, 370, 387, 328, 330, 240, 330, 400, 451, 482, 497, 490, 472, 428, 380, 300, 425, 500, 581, 602, 642, 610, 612, 528, 495, 360

Offset

1,3

Links

Table of n, a(n) for n=1..59.

Formula

a(n) = Sum_{k=1..floor(n/2)} (k mod 10) * ((n-k) mod 10).

Example

a(20) = 165; There are 10 ways to write 20 as the sum of two positive integers: (19,1), (18,2), (17,3), (16,4), (15,5), (14,6), (13,7), (12,8), (11,9), and (10,10). Using the final digits from each pair as the side lengths of the rectangles, the combined area is 9*1 + 8*2 + 7*3 + 6*4 + 5*5 + 4*6 + 3+7 + 2*8 + 1*9 + 0*0 = 165.

Mathematica

Table[Sum[Mod[k, 10]*Mod[n - k, 10], {k, Floor[n/2]}], {n, 60}]

Crossrefs

Cf. A010879, A023855.

Sequence in context: A049830 A270879 A022302 * A023855 A191832 A066964

Adjacent sequences: A345023 A345024 A345025 * A345027 A345028 A345029

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 06 2021

Status

approved