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A024598 a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = floor((n+1)/2), s = (odd natural numbers). 2
1, 3, 14, 22, 55, 73, 140, 172, 285, 335, 506, 578, 819, 917, 1240, 1368, 1785, 1947, 2470, 2670, 3311, 3553, 4324, 4612, 5525, 5863, 6930, 7322, 8555, 9005, 10416, 10928, 12529, 13107, 14910, 15558, 17575, 18297, 20540, 21340, 23821, 24703, 27434, 28402 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sum of the areas of all rectangles with odd side lengths r and s such that r + s = 2n. - Wesley Ivan Hurt, Apr 21 2020

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

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

FORMULA

a(n) = (4*n^3 + 3*n^2 + 2*n - 3*n^2*(-1)^n)/12. - Luce ETIENNE, Jan 17 2015

G.f.: x*(3*x^4 + 2*x^3 + 8*x^2 + 2*x + 1) / ((x-1)^4*(x+1)^3). - Colin Barker, Jan 17 2015

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

MATHEMATICA

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 3, 14, 22, 55, 73, 140}, 50] (* Harvey P. Dale, Aug 30 2021 *)

PROG

(PARI) Vec(x*(3*x^4+2*x^3+8*x^2+2*x+1)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Jan 17 2015

(PARI) odd(n) = 2*n-1;

a(n) = sum(j=1, (n+1)\2, odd(j)*odd(n+1-j)); \\ Michel Marcus, Jan 17 2015

CROSSREFS

Sequence in context: A255219 A226341 A024473 * A019001 A034103 A034113

Adjacent sequences:  A024595 A024596 A024597 * A024599 A024600 A024601

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 6 15:57 EST 2021. Contains 349565 sequences. (Running on oeis4.)