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).

3, 5, 22, 30, 73, 91, 172, 204, 335, 385, 578, 650, 917, 1015, 1368, 1496, 1947, 2109, 2670, 2870, 3553, 3795, 4612, 4900, 5863, 6201, 7322, 7714, 9005, 9455, 10928, 11440, 13107, 13685, 15558, 16206, 18297, 19019, 21340, 22140, 24703, 25585, 28402, 29370, 32453

Offset

2,1

Comments

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

Links

Table of n, a(n) for n=2..46.

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

a(n) = n*(4*n^2 - 3*n + 2 + 3*n*(-1)^n)/12. - Luce ETIENNE, Jan 07 2015

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

a(n) = Sum_{i=1..n-1} i * (2*n-i) * (i mod 2). - Wesley Ivan Hurt, Apr 21 2020

Example

For n=2, k=1, and a(n) = s(1)*s(2) = 1*3 = 3.

Maple

seq( n*(4*n^2 - 3*n + 2 + 3*n*(-1)^n)/12, n=2..30); # Robert Israel, Jan 13 2015

Prog

(PARI) vector(40, n, sum(k=1, n\2, (2*k-1)*(2*(n-k+1)-1))) \\ Michel Marcus, Jan 07 2015
(PARI) a(n)=n*(2*n^2 - n%2*3*n + 1)/6 \\ Charles R Greathouse IV, Jan 15 2015

Crossrefs

Sequence in context: A147442 A370580 A025093 * A203192 A025098 A025117

Adjacent sequences: A025109 A025110 A025111 * A025113 A025114 A025115

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Offset corrected by Michel Marcus, Jan 13 2015

Status

approved