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A022288 a(n) = n*(31*n-1)/2. 15

%I

%S 0,15,61,138,246,385,555,756,988,1251,1545,1870,2226,2613,3031,3480,

%T 3960,4471,5013,5586,6190,6825,7491,8188,8916,9675,10465,11286,12138,

%U 13021,13935,14880,15856,16863,17901

%N a(n) = n*(31*n-1)/2.

%H Harvey P. Dale, <a href="/A022288/b022288.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = 31*n + a(n-1) - 16 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010

%F a(0)=0, a(1)=15, a(2)=61; for n>2, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Mar 31 2014

%F G.f.: x*(15 + 16*x)/(1 - x)^3. - _R. J. Mathar_, Sep 02 2016

%F a(n) = A000217(16*n-1) - A000217(15*n-1). In general, n*((2*k+1)*n - 1)/2 = A000217((k+1)*n-1) - A000217(k*n-1), and the ordinary generating function is x*(k + (k+1)*x)/(1 - x)^3. - _Bruno Berselli_, Oct 14 2016

%F E.g.f.: (x/2)*(31*x + 30)*exp(x). - _G. C. Greubel_, Aug 24 2017

%t Table[n (31 n - 1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 15, 61}, 40] (* _Harvey P. Dale_, Mar 31 2014 *)

%o (PARI) a(n)=n*(31*n-1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A000217, A022289.

%Y Cf. similar sequences of the form n*((2*k+1)*n - 1)/2: A161680 (k=0), A000326 (k=1), A005476 (k=2), A022264 (k=3), A022266 (k=4), A022268 (k=5), A022270 (k=6), A022272 (k=7), A022274 (k=8), A022276 (k=9), A022278 (k=10), A022280 (k=11), A022282 (k=12), A022284 (k=13), A022286 (k=14), this sequence (k=15).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified February 20 16:36 EST 2020. Contains 332080 sequences. (Running on oeis4.)