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A070333 Expansion of (1+x)*(1-x+x^2)/( (1-x)^4*(1+x+x^2) ). 1
1, 3, 6, 12, 21, 33, 50, 72, 99, 133, 174, 222, 279, 345, 420, 506, 603, 711, 832, 966, 1113, 1275, 1452, 1644, 1853, 2079, 2322, 2584, 2865, 3165, 3486, 3828, 4191, 4577, 4986, 5418, 5875, 6357, 6864, 7398, 7959, 8547, 9164, 9810, 10485 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of 3 X 3 matrices with nonnegative integer entries such that every row sum, column sum and the trace of the matrix is n. - Sharon Sela (sharonsela(AT)hotmail.com), May 20 2002

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,3,-1).

FORMULA

a(n) = 1 +7*n/6 +n^2/2 +n^3/9 +2*A049347(n-1)/9. - R. J. Mathar, Dec 03 2010

From Mircea Merca, Dec 03 2010: (Start)

a(n) = round((2*n+3)*(n^2+3*n+6)/18).

a(n) = floor((n+2)*(2*n^2+5*n+11)/18).

a(n) = ceiling((n+1)*(2*n^2+7*n+14)/18).

a(n) = round((n+1)*(2*n^2+7*n+14)/18).

a(n) = a(n-3)+n^2+2, n>2.  (End)

MAPLE

A049347 := proc(n) op(1+(n mod 3), [1, -1, 0]) ; end proc:

A070333 := proc(n) 1+7*n/6+n^2/2+n^3/9+2*A049347(n-1)/9 ; end proc: # R. J. Mathar, Dec 03 2010

MATHEMATICA

CoefficientList[ Series[(1 + x^3)/(1 - 3*x + 3*x^2 - 2*x^3 + 3*x^4 - 3*x^5 + x^6), {x, 0, 45}], x]

PROG

(MAGMA) [Round((2*n+3)*(n^2+3*n+6)/18): n in [0..50]]; // Vincenzo Librandi, Jun 25 2011

(PARI) Vec((1+x)*(1-x+x^2)/((1-x)^4*(1+x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

CROSSREFS

Cf. A059827, A001844, A002817.

Sequence in context: A246866 A053479 A290768 * A011779 A161809 A084439

Adjacent sequences:  A070330 A070331 A070332 * A070334 A070335 A070336

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 11 2002

STATUS

approved

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Last modified July 26 15:27 EDT 2021. Contains 346294 sequences. (Running on oeis4.)