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A023857 a(n) = s(1)t(n)+s(2)t(n-1)+...+s(k)t(n+1-k), where k=floor((n+1)/2), s = (natural numbers), t = (natural numbers >= 3). 5
3, 4, 13, 16, 34, 40, 70, 80, 125, 140, 203, 224, 308, 336, 444, 480, 615, 660, 825, 880, 1078, 1144, 1378, 1456, 1729, 1820, 2135, 2240, 2600, 2720, 3128, 3264, 3723, 3876, 4389, 4560, 5130, 5320, 5950, 6160, 6853, 7084, 7843, 8096, 8924, 9200, 10100, 10400, 11375, 11700 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..50.

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

FORMULA

a(n) = sum_{i=1..ceil(n/2)} i*(n-i+3) = -ceil(n/2) *(ceil(n/2)+1) *(2*ceil(n/2)-3n-8)/6. - Wesley Ivan Hurt, Sep 20 2013

G.f. x*(3+x) / ( (1+x)^3*(x-1)^4 ). - R. J. Mathar, Sep 25 2013

a(n) = 3*A058187(n-1)+A058187(n-2). - R. J. Mathar, Sep 25 2013

a(n) = (4*n^3+27*n^2+50*n+21-3*(n^2+6*n+7)*(-1)^n)/48. - Luce ETIENNE, Nov 21 2014

MAPLE

seq(sum(i*(n-i+3), i=1..ceil(n/2)), n=1..20); # Wesley Ivan Hurt, Sep 20 2013

MATHEMATICA

Table[-Ceiling[n/2]*(Ceiling[n/2]+1)*(2*Ceiling[n/2]-3n-8)/6, {n, 100}] (* Wesley Ivan Hurt, Sep 20 2013 *)

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {3, 4, 13, 16, 34, 40, 70}, 50] (* Harvey P. Dale, Feb 13 2018 *)

CROSSREFS

Cf. A023855, A023856, A024305, A024854.

Sequence in context: A087884 A057570 A024853 * A291250 A205901 A302392

Adjacent sequences:  A023854 A023855 A023856 * A023858 A023859 A023860

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 16 14:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)