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a(n) = n*(19*n + 1)/2.
3

%I #39 Sep 08 2022 08:44:46

%S 0,10,39,87,154,240,345,469,612,774,955,1155,1374,1612,1869,2145,2440,

%T 2754,3087,3439,3810,4200,4609,5037,5484,5950,6435,6939,7462,8004,

%U 8565,9145,9744,10362,10999,11655,12330,13024,13737,14469,15220,15990,16779,17587,18414

%N a(n) = n*(19*n + 1)/2.

%H G. C. Greubel, <a href="/A022277/b022277.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 19*n + a(n-1) - 9 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010

%F G.f.: x*(10 + 9*x)/(1 - x)^3. - _Vincenzo Librandi_, Mar 31 2015

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - _Vincenzo Librandi_, Mar 31 2015

%F a(n) = A022276(-n). - _Bruno Berselli_, Apr 01 2015

%F a(n) = A000217(10*n) - A000217(9*n). - _Bruno Berselli_, Oct 13 2016

%F E.g.f.: (x/2)*(19*x + 20)*exp(x). - _G. C. Greubel_, Aug 23 2017

%t Table[n (19 n + 1)/2, {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 07 2011 *)

%t CoefficientList[Series[x (10 + 9 x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 31 2015 *)

%t LinearRecurrence[{3,-3,1},{0,10,39},50] (* _Harvey P. Dale_, May 02 2021 *)

%o (PARI) a(n)=n*(19*n+1)/2 \\ _Charles R Greathouse IV_, Mar 07 2011

%o (Magma) [n*(19*n + 1)/2: n in [0..45]]; // _Vincenzo Librandi_, Mar 31 2015

%Y Cf. A022276.

%Y Cf. similar sequences listed in A022289.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Mar 31 2015