A121509 - OEIS

%I #23 Oct 17 2020 18:46:39

%S 1,3,11,23,41,63,91,123,161,203,251,303,361,423,491,563,641,723,811,

%T 903,1001,1103,1211,1323,1441,1563,1691,1823,1961,2103,2251,2403,2561,

%U 2723,2891,3063,3241,3423,3611,3803,4001,4203,4411,4623,4841,5063,5291,5523

%N a(n) = 5*n^2/2 - 5*n + 13/4 - (-1)^n/4.

%H Colin Barker, <a href="/A121509/b121509.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

%F a(n) = 1 + 2*(n-1)^2 + floor((n-1)^2/2). - _Wesley Ivan Hurt_, Jun 14 2013

%F G.f.: x*(1 + x + 5*x^2 + 3*x^3) / ((1 - x)^3*(1 + x)). - _Colin Barker_, Jun 08 2020

%t LinearRecurrence[{2,0,-2,1},{1,3,11,23},50] (* _Harvey P. Dale_, Oct 17 2020 *)

%o (PARI) a(n) = 5*n^2/2 - 5*n + 13/4 - (-1)^n/4; \\ _Jinyuan Wang_, Jun 07 2020

%o (PARI) Vec(x*(1 + x + 5*x^2 + 3*x^3) / ((1 - x)^3*(1 + x)) + O(x^40)) \\ _Colin Barker_, Jun 08 2020

%Y Cf. A001849, A003215, A005448.

%K nonn,easy

%O 1,2

%A _Roger L. Bagula_, Sep 07 2006

%E Definition replaced by polynomial - The Assoc. Editors of the OEIS, Oct 14 2009