OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(5+2*x)/(1-x)^3.
a(n) - a(-n) = A008585(n).
a(n) + a(-n) = A033582(n).
n*a(n+1) - (n+1)*a(n) = A024966(n). - Bruno Berselli, May 30 2012
n*a(n+2) - (n+2)*a(n) = A067727(n) for n>0. - Bruno Berselli, May 30 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2, a(0)=0, a(1)=5, a(2)=17. - Philippe Deléham, Mar 26 2013
a(n) = A174738(7*n+4). - Philippe Deléham, Mar 26 2013
E.g.f.: (1/2)*(7*x^2 + 10*x)*exp(x). - G. C. Greubel, Jul 17 2017
EXAMPLE
From Ilya Gutkovskiy, Mar 31 2016: (Start)
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.
. n=1 n=2 n=3 n=4
(End)
MATHEMATICA
Table[(n - 1) (7 n - 4)/2, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
LinearRecurrence[{3, -3, 1}, {0, 5, 17}, 50] (* Harvey P. Dale, Sep 07 2022 *)
PROG
(Magma) [n*(7*n+3)/2: n in [0..44]];
(PARI) a(n)=n*(7*n+3)/2 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Feb 11 2011
STATUS
approved