Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #26 Apr 22 2020 01:46:53
%S 3,5,22,30,73,91,172,204,335,385,578,650,917,1015,1368,1496,1947,2109,
%T 2670,2870,3553,3795,4612,4900,5863,6201,7322,7714,9005,9455,10928,
%U 11440,13107,13685,15558,16206,18297,19019,21340,22140,24703,25585,28402,29370,32453
%N a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = floor(n/2), s = (odd natural numbers).
%C Sum of the areas of all rectangles with distinct odd side lengths r and s such that r + s = 2n. - _Wesley Ivan Hurt_, Apr 21 2020
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F a(n) = n*(4*n^2 - 3*n + 2 + 3*n*(-1)^n)/12. - _Luce ETIENNE_, Jan 07 2015
%F G.f.: x^2*(3 + 2*x + 8*x^2 + 2*x^3 + x^4)/((1+x)^3*(1-x)^4). - _Robert Israel_, Jan 13 2015
%F a(n) = Sum_{i=1..n-1} i * (2*n-i) * (i mod 2). - _Wesley Ivan Hurt_, Apr 21 2020
%e For n=2, k=1, and a(n) = s(1)*s(2) = 1*3 = 3.
%p seq( n*(4*n^2 - 3*n + 2 + 3*n*(-1)^n)/12, n=2..30); # _Robert Israel_, Jan 13 2015
%o (PARI) vector(40, n, sum(k=1, n\2, (2*k-1)*(2*(n-k+1)-1))) \\ _Michel Marcus_, Jan 07 2015
%o (PARI) a(n)=n*(2*n^2 - n%2*3*n + 1)/6 \\ _Charles R Greathouse IV_, Jan 15 2015
%K nonn,easy
%O 2,1
%A _Clark Kimberling_
%E Offset corrected by _Michel Marcus_, Jan 13 2015