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A100536 a(n) = 3*n^2 - 2. 13
1, 10, 25, 46, 73, 106, 145, 190, 241, 298, 361, 430, 505, 586, 673, 766, 865, 970, 1081, 1198, 1321, 1450, 1585, 1726, 1873, 2026, 2185, 2350, 2521, 2698, 2881, 3070, 3265, 3466, 3673, 3886, 4105, 4330, 4561, 4798, 5041, 5290, 5545, 5806, 6073, 6346, 6625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

n such that 3*n+6 is a perfect square. - Gary Detlefs, Feb 22 2010

-a(n) = (k-1)^2 + k^2 + (k+1)^2, where k = n*sqrt(-1). - Bruno Berselli, Jan 24 2014

Binomial transform of (1, 9, 6, 0, 0, 0, 0, 0, 0, 0, ...). - Philippe Deléham, Mar 16 2014

a(T(n)+1) = T(n+1)^2 + T(n)^2 + T(n-1)^2, where T = A000217. - Bruno Berselli, May 14 2014

LINKS

Table of n, a(n) for n=1..47.

A. J. C. Cunningham, Factorisation of N and N' = (x^n -+ y^n) / (x -+ y [when x-y=n], Messenger Math., 54 (1924), 17-21 [Incomplete annotated scanned copy]

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

FORMULA

a(n) = a(n-1) + 6*n - 3 for n>1. - Vincenzo Librandi, Nov 17 2010

G.f.: x*(1+7*x-2*x^2) / (1-x)^3. - R. J. Mathar, Oct 03 2011

a(n+1) = binomial(n,0) + 9*binomial(n,1) + 6*binomial(n,2). - Philippe Deléham, Mar 16 2014

a(n) = floor(1/(n*tan(1/n) - 1)). - Clark Kimberling, Dec 02 2014

EXAMPLE

a(2)=10 after the evaluation of a(2)=3(2^2)-2=3(4)-2=12-2=10.

a(1) = 1*1 = 1;

a(2) = 1*1 + 9*1 = 10;

a(3) = 1*1 + 9*2 + 6*1 = 25;

a(4) = 1*1 + 9*3 + 6*3 = 46;

a(5) = 1*1 + 9*4 + 6*6 = 73; etc. - Philippe Deléham, Mar 16 2014

MATHEMATICA

3*Range[50]^2-2 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

PROG

(PARI) a(n)=3*n^2-2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000124, A054000.

Sequence in context: A043123 A043903 A163631 * A024838 A020179 A022670

Adjacent sequences:  A100533 A100534 A100535 * A100537 A100538 A100539

KEYWORD

nonn,easy

AUTHOR

Tyler J Newman (Tylerjnewman(AT)adelphia.net), Nov 27 2004

STATUS

approved

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Last modified November 20 10:41 EST 2017. Contains 294963 sequences.