A202141 - OEIS

%I #25 Oct 21 2024 04:39:01

%S 5,2,25,74,149,250,377,530,709,914,1145,1402,1685,1994,2329,2690,3077,

%T 3490,3929,4394,4885,5402,5945,6514,7109,7730,8377,9050,9749,10474,

%U 11225,12002,12805,13634,14489,15370,16277,17210,18169,19154,20165,21202,22265

%N a(n) = 13*n^2 - 16*n + 5.

%C Numbers of the form (r*n - r + 1)^2 + ((r+1)*n - r)^2; in this case, r=2.

%C Inverse binomial transform of this sequence: 5,-3, 26, 0, 0 (0 continued).

%H Bruno Berselli, <a href="/A202141/b202141.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.: (5 - 13*x + 34*x^2)/(1-x)^3.

%F a(n) = A161587(n-1) + 1 with A161587(-1) = 4.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. - _Wesley Ivan Hurt_, Oct 09 2017

%F E.g.f.: (5 - 3*x + 13*x^2)*exp(x). - _Elmo R. Oliveira_, Oct 20 2024

%p A202141:=n->13*n^2-16*n+5: seq(A202141(n), n=0..100); # _Wesley Ivan Hurt_, Oct 09 2017

%t Table[13 n^2 - 16 n + 5, {n, 0, 42}]

%o (PARI) for(n=0, 42, print1(13*n^2-16*n+5", "));

%o (Magma) [13*n^2-16*n+5: n in [0..42]];

%Y Cf. A190816 (r=1), A154355 (r=3), A161587.

%K nonn,easy

%O 0,1

%A _Bruno Berselli_, Dec 12 2011