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A024305 a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k=[ (n+1)/2) ] and s = (natural numbers >= 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

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). Recurrence: 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. - Vladeta Jovovic, Jan 01 2003

a(n) = sum_{i=1..ceil(n/2)} (i+1)*(n-i+2) = ceil(n/2)*(-2*ceil(n/2)^2+3n*ceil(n/2)+9n+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 * A034492 A125691 A270270

Adjacent sequences:  A024302 A024303 A024304 * A024306 A024307 A024308

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 20 02:47 EST 2018. Contains 299357 sequences. (Running on oeis4.)