A298037 - OEIS

%I #24 Jul 20 2024 14:37:25

%S 1,13,25,61,85,145,181,265,313,421,481,613,685,841,925,1105,1201,1405,

%T 1513,1741,1861,2113,2245,2521,2665,2965,3121,3445,3613,3961,4141,

%U 4513,4705,5101,5305,5725,5941,6385,6613,7081,7321,7813,8065,8581,8845,9385,9661

%N Partial sums of A298036.

%H Hakan Icoz, <a href="/A298037/b298037.txt">Table of n, a(n) for n = 0..20000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F From _Joerg Arndt_, Aug 23 2020: (Start)

%F G.f.: (1 + 12*x + 10*x^2 + 12*x^3 + x^4)/((1 - x^2)^2*(1-x)).

%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). (End)

%F a(n)= A298036(n) + a(n-1). - _Hakan Icoz_, Aug 23 2020

%e a(1) = 12 + 1 = 13

%e a(2) = 12 + 13 = 25

%e a(3) = 36 + 25 = 61

%t LinearRecurrence[{1, 2, -2, -1, 1}, {1, 13, 25, 61, 85}, 100] (* _Paolo Xausa_, Jul 20 2024 *)

%Y Cf. A298036.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jan 22 2018

%E a(7)-a(50) from _Hakan Icoz_, Aug 22 2020