A298030 - OEIS

%I #14 Aug 20 2023 10:51:21

%S 1,4,10,22,40,73,112,163,220,289,364,451,544,649,760,883,1012,1153,

%T 1300,1459,1624,1801,1984,2179,2380,2593,2812,3043,3280,3529,3784,

%U 4051,4324,4609,4900,5203,5512,5833,6160,6499,6844,7201,7564,7939,8320,8713,9112,9523,9940,10369,10804,11251,11704

%N Partial sums of A298029.

%H Colin Barker, <a href="/A298030/b298030.txt">Table of n, a(n) for n = 0..1000</a>

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

%F G.f.: -(3*x^7 - 9*x^5 - 3*x^4 - 4*x^3 - 2*x^2 - 2*x - 1)/((1 - x)^2*(1 - x^2)).

%F From _Colin Barker_, Jan 25 2018: (Start)

%F a(n) = (9*n^2 - 18*n + 8) / 2 for n>3 and even.

%F a(n) = (9*n^2 - 18*n + 11) / 2 for n>3 and odd.

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

%F E.g.f.: ((8 - 9*x + 9*x^2)*cosh(x) + (11 - 9*x + 9*x^2)*sinh(x) - 6 + 6*x + 6*x^2 + x^3)/2. - _Stefano Spezia_, Aug 19 2023

%o (PARI) Vec((1 + 2*x + 2*x^2 + 4*x^3 + 3*x^4 + 9*x^5 - 3*x^7) / ((1 - x)^3*(1 + x)) + O(x^50)) \\ _Colin Barker_, Jan 25 2018

%Y Cf. A298029.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jan 21 2018