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A136008 a(n) = n^6 - n^2. 1
0, 0, 60, 720, 4080, 15600, 46620, 117600, 262080, 531360, 999900, 1771440, 2985840, 4826640, 7529340, 11390400, 16776960, 24137280, 34011900, 47045520, 63999600, 85765680, 113379420, 148035360, 191102400, 244140000, 308915100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

G.f.: (60*x^5 + 300*x^4 + 300*x^3 + 60*x^2)/(-x^7 + 7*x^6 - 21*x^5 + 35*x^4 - 35*x^3 + 21*x^2 - 7*x + 1). - Alexander R. Povolotsky, Apr 01 2008

a(n) = A001014(n) - A000290(n). - Omar E. Pol, Dec 26 2008

From Amiram Eldar, Jan 12 2021: (Start)

Sum_{n>=2} 1/a(n) = 7/8 - Pi^2/6 + Pi*coth(Pi)/4.

Sum_{n>=2} (-1)^n/a(n) = -7/8 + Pi^2/12 + Pi*csch(Pi)/4 = -7/8 + A072691 + (1/4) * A090986. (End)

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, May 04 2021

MATHEMATICA

f[n_]:=n^6-n^2; f[Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2011 *)

PROG

(Sage) [lucas_number1(3, n^3, n^2) for n in range(0, 31)] # Zerinvary Lajos, Jul 16 2008

CROSSREFS

Cf. A000290, A001014. - Omar E. Pol, Dec 26 2008

Cf. A013661, A072691, A090986.

Sequence in context: A268624 A088945 A269189 * A000555 A034865 A138409

Adjacent sequences:  A136005 A136006 A136007 * A136009 A136010 A136011

KEYWORD

easy,nonn

AUTHOR

Rolf Pleisch, Mar 16 2008

EXTENSIONS

Extended by Ray Chandler, Dec 13 2008

STATUS

approved

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Last modified December 4 19:40 EST 2021. Contains 349526 sequences. (Running on oeis4.)