A135703 - OEIS

%I #37 Sep 08 2022 08:45:32

%S 0,5,24,57,104,165,240,329,432,549,680,825,984,1157,1344,1545,1760,

%T 1989,2232,2489,2760,3045,3344,3657,3984,4325,4680,5049,5432,5829,

%U 6240,6665,7104,7557,8024,8505,9000,9509,10032,10569,11120,11685,12264,12857,13464

%N a(n) = n*(7*n-2).

%H G. C. Greubel, <a href="/A135703/b135703.txt">Table of n, a(n) for n = 0..2500</a>

%H L. Hogben, <a href="https://archive.org/details/chanceandchoiceb029729mbp/page/n39">Choice and Chance by Cardpack and Chessboard</a>, Vol. 1, Max Parrish and Co, London, 1950, p. 36.

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

%F a(n) = 5*n + 14*binomial(n,2).

%F From _R. J. Mathar_, Apr 21 2008: (Start)

%F O.g.f. x*(5+9*x)/(1-x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

%F a(n) = a(n-1) + 14*n - 9 (with a(0)=0). - _Vincenzo Librandi_, Nov 24 2010

%F a(n) = 4*A000217(n) + A051624(n). - _Bruno Berselli_, Feb 11 2011

%F E.g.f.: x*(5 + 7*x)*exp(x). - _G. C. Greubel_, Oct 29 2016

%t Array[ #*(7*# - 2) &, 50, 0] (* _Zerinvary Lajos_, Jul 10 2009 *)

%o (PARI) a(n)=n*(7*n-2) \\ _Charles R Greathouse IV_, Oct 07 2015

%o (Magma) [n*(7*n-2): n in [0..50]]; // _G. C. Greubel_, Jul 04 2019

%o (Sage) [n*(7*n-2) for n in (0..50)] # _G. C. Greubel_, Jul 04 2019

%o (GAP) List([0..50], n-> n*(7*n-2)) # _G. C. Greubel_, Jul 04 2019

%Y Cf. index to numbers of the form n*(d*n+10-d)/2 in A014106.

%Y Cf. A185019.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Mar 04 2008