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A155753 (n^3 - n + 9)/3. 2
3, 5, 11, 23, 43, 73, 115, 171, 243, 333, 443, 575, 731, 913, 1123, 1363, 1635, 1941, 2283, 2663, 3083, 3545, 4051, 4603, 5203, 5853, 6555, 7311, 8123, 8993, 9923, 10915, 11971, 13093, 14283, 15543, 16875, 18281, 19763, 21323, 22963 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n)+a(n-1)=2*A153057(n-1) (n>1); a(n)+A000217(n)=A153057(n) (n>0). [From Bruno Berselli, Jun 21 2010]

LINKS

B. Berselli, Table of n, a(n) for n = 1..10000.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n)=n(n-1)+a(n-1), with a(1)=3 .

Contribution from Bruno Berselli, Jun 21 2010: (Start)

G.f.: x*(3-9*x+11*x^2-3*x^3)/(1-x)^4.

a(n)-4*a(n-1)+6*a(n-2)-4*a(n-3)+a(n-4) = 0 with n>4.

a(n) = 3+A007290(n+1) = (n^3-n+9)/3. (End)

MATHEMATICA

f[n_]:=(n^3 - n + 9)/3; f[Range[1, 100]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2011*)

LinearRecurrence[{4, -6, 4, -1}, {3, 5, 11, 23}, 50] (* Harvey P. Dale, Oct 20 2011 *)

PROG

(PARI) a(n)=(n^3-n)/3+3 \\ Charles R Greathouse IV, Jan 11 2012

CROSSREFS

Sequence in context: A280773 A109927 A146276 * A133914 A169913 A260239

Adjacent sequences:  A155750 A155751 A155752 * A155754 A155755 A155756

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jan 26 2009

EXTENSIONS

Entries confirmed by John W. Layman, Jun 17 2010.

Edited by Bruno Berselli, Aug 12 2010

New name from Charles R Greathouse IV, Jan 11 2012

STATUS

approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)