A298367 - OEIS

%I #199 Jun 25 2020 19:18:34

%S 1,2,5,14,42,90,213,527,1326,3317,8022,19608,48272,119073,293109,

%T 719074,1766201,4342666,10679582,26253546,64516501,158569355,

%U 389788182,958172417,2355231458,5789058028,14229546200,34976963777,85975197161,211329783890,519453451997

%N Number of (n + 1, n + 2)-core partitions with each part repeated at most four times.

%H Anthony Zaleski, Doron Zeilberger, <a href="https://arxiv.org/abs/1712.10072">On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts</a>, arXiv:1712.10072 [math.CO], 2017.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 2, 5, 14).

%F G.f.: -(14*x^4+5*x^3+2*x^2+x+1)/(14*x^5+5*x^4+2*x^3+x^2+x-1).

%t LinearRecurrence[{1, 1, 2, 5, 14}, {1, 2, 5, 14, 42}, 40] (* _Jean-François Alcover_, Feb 20 2018 *)

%t CoefficientList[ Series[-(14x^4 + 5x^3 + 2x^2 + x + 1)/(14x^5 + 5x^4 + 2x^3 + x^2 + x - 1), {x, 0, 33}], x] (* _Robert G. Wilson v_, Feb 24 2018 *)

%o (PARI) x='x+O('x^99); Vec((1+x+2*x^2+5*x^3+14*x^4)/(1-x-x^2-2*x^3-5*x^4-14*x^5)) \\ _Altug Alkan_, Mar 03 2018

%K nonn,easy

%O 0,2

%A _Anthony Zaleski_, Feb 15 2018