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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
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 (list; graph; refs; listen; history; text; internal format)
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: A292557 A147442 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

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Last modified June 27 19:31 EDT 2022. Contains 354898 sequences. (Running on oeis4.)