A244630 - OEIS

%I #37 Dec 02 2024 18:11:02

%S 0,17,68,153,272,425,612,833,1088,1377,1700,2057,2448,2873,3332,3825,

%T 4352,4913,5508,6137,6800,7497,8228,8993,9792,10625,11492,12393,13328,

%U 14297,15300,16337,17408,18513,19652,20825,22032,23273,24548,25857,27200,28577,29988

%N a(n) = 17*n^2.

%C First bisection of A195047. - _Bruno Berselli_, Jul 03 2014

%C Norms of purely imaginary numbers in Z[sqrt(-17)] (for example, 3*sqrt(-17) has norm 153). - _Alonso del Arte_, Jun 23 2018

%H Vincenzo Librandi, <a href="/A244630/b244630.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 G.f.: 17*x*(1 + x)/(1 - x)^3. [corrected by _Bruno Berselli_, Jul 03 2014]

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

%F a(n) = 17*A000290(n). - _Omar E. Pol_, Jul 03 2014

%F a(n) = a(-n). - _Muniru A Asiru_, Jun 29 2018

%F From _Elmo R. Oliveira_, Dec 02 2024: (Start)

%F E.g.f.: 17*x*(1 + x)*exp(x).

%F a(n) = n*A008599(n) = A195047(2*n). (End)

%p seq(17*n^2,n=0..45); # _Muniru A Asiru_, Jun 29 2018

%t Table[17 n^2, {n, 0, 40}]

%o (Magma) [17*n^2: n in [0..40]];

%o (PARI) a(n)=17*n^2 \\ _Charles R Greathouse IV_, Oct 07 2015

%o (GAP) List([0..45],n->17*n^2); # _Muniru A Asiru_, Jun 29 2018

%o (Scala) for (i <- 0 to 50) yield 17 * (i * i) // _Alonso del Arte_, Jun 29 2018

%Y Cf. A008599, A195047.

%Y Cf. similar sequences of the type k*n^2: A000290 (k = 1), A001105 (k = 2), A033428 (k = 3), A016742 (k = 4), A033429 (k = 5), A033581 (k = 6), A033582 (k = 7), A139098 (k = 8), A016766 (k = 9), A033583 (k = 10), A033584 (k = 11), A135453 (k = 12),  A152742 (k = 13), A144555 (k = 14), A064761 (k = 15), A016802 (k = 16), this sequence (k = 17), A195321 (k = 18), A244631 (k = 19), A195322 (k = 20), A064762 (k = 21), A195323 (k = 22), A244632 (k = 23), A195824 (k = 24), A016850 (k = 25), A244633 (k = 26), A244634 (k = 27), A064763 (k = 28), A244635 (k = 29), A244636 (k = 30).

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jul 03 2014