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A025112 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). 0

%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

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)