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A190798 Maximum value of k^2 * (n-k). 1
0, 0, 1, 4, 9, 18, 32, 50, 75, 108, 147, 196, 256, 324, 405, 500, 605, 726, 864, 1014, 1183, 1372, 1575, 1800, 2048, 2312, 2601, 2916, 3249, 3610, 4000, 4410, 4851, 5324, 5819, 6348, 6912, 7500, 8125, 8788, 9477, 10206, 10976, 11774, 12615, 13500, 14415, 15376, 16384, 17424, 18513, 19652, 20825, 22050, 23328, 24642, 26011, 27436, 28899, 30420, 32000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

FORMULA

a(n) = k^2 * (n-k), where k = round(2*n/3).

a(3*n) = 4*n^3, a(3*n-1) = n*(2*n-1)^2, a(3*n+1) = n*(2*n+1)^2.

O.g.f.: x^2*(1+x)^2*(1+x^2)/((1-x)^4*(1+x+x^2)^2).

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) - a(n-6) + 2*a(n-7) - a(n-8) for n >= 8.

a(-n) = -a(n). - Michael Somos, May 22 2011

MATHEMATICA

CoefficientList[Series[x^2*(1+x)^2*(1+x^2)/((1-x)^4*(1+x+x^2)^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 13 2018 *)

PROG

(PARI) a(n)=my(k=2*n\/3); k^2*(n-k) \\ Charles R Greathouse IV, May 20 2011

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0, 0] cat Coefficients(R!(x^2*(1+x)^2*(1+x^2)/((1-x)^4*(1+x+x^2)^2))); // G. C. Greubel, Aug 13 2018

CROSSREFS

Cf. A002620 (max of k * (n-k)).

Sequence in context: A047959 A047960 A301090 * A009917 A301095 A301259

Adjacent sequences:  A190795 A190796 A190797 * A190799 A190800 A190801

KEYWORD

nonn,easy

AUTHOR

Franklin T. Adams-Watters, May 20 2011

STATUS

approved

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Last modified September 20 19:27 EDT 2021. Contains 347589 sequences. (Running on oeis4.)