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A024305 a(n) = 2*(n+1) + 3*n + ... + (k+1)*(n+2-k), where k = floor((n+1)/2). 5
4, 6, 17, 22, 43, 52, 86, 100, 150, 170, 239, 266, 357, 392, 508, 552, 696, 750, 925, 990, 1199, 1276, 1522, 1612, 1898, 2002, 2331, 2450, 2825, 2960, 3384, 3536, 4012, 4182, 4713, 4902, 5491, 5700, 6350, 6580, 7294, 7546, 8327, 8602, 9453, 9752, 10676, 11000, 12000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..49.

FORMULA

From Vladeta Jovovic, Jan 01 2003: (Start)

a(n) = (1/48)*(4*n^3 + (3*(-1)^(n+1) + 39)*n^2 + (18*(-1)^(n+1) + 74)*n + 27*(-1)^(n+1) + 27).

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).

G.f.: x*(4 + 2*x - x^2 - x^3)/((1+x)^3*(1-x)^4). (End)

a(n) = Sum_{i=1..ceiling(n/2)} (i+1)*(n-i+2) = ceiling(n/2)*(-2*ceiling(n/2)^2 + 3n*ceiling(n/2) + 9*n + 14)/6. - Wesley Ivan Hurt, Sep 20 2013

MAPLE

seq(sum((i+1)*(k-i+2), i=1..ceil(k/2)), k=1..70); # Wesley Ivan Hurt, Sep 20 2013

MATHEMATICA

Table[Ceiling[n/2]*(-2*Ceiling[n/2]^2+3n*Ceiling[n/2]+9n+14)/6, {n, 100}] (* Wesley Ivan Hurt, Sep 20 2013 *)

CROSSREFS

Bisection: 2*A051925(n).

Cf. A023855, A023856, A023857, A024854, A024868.

Sequence in context: A226631 A226634 A105271 * A320245 A034492 A125691

Adjacent sequences:  A024302 A024303 A024304 * A024306 A024307 A024308

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Name simplified by Jon E. Schoenfield, Jun 12 2019

STATUS

approved

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Last modified May 28 01:48 EDT 2020. Contains 334671 sequences. (Running on oeis4.)