A390044 - OEIS

%I #23 Jan 16 2026 02:46:54

%S 1,4,10,20,35,57,92,156,285,550,1079,2092,3965,7359,13485,24633,45185,

%T 83488,155248,289656,540536,1006897,1871236,3471298,6434484,11928731,

%U 22128873,41080980,76302420,141745045,263289438,488945055,907802332,1685254125,3128438335

%N Expansion of 1 / ((1-x)^4 - x^5).

%H Seiichi Manyama, <a href="/A390044/b390044.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,1).

%F a(n) = Sum_{k=0..floor(n/5)} binomial(n-k+3,n-5*k).

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5).

%t LinearRecurrence[{4,-6,4,-1,1},{1,4,10,20,35},50] (* _Vincenzo Librandi_, Jan 16 2026 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^4-x^5))

%o (Magma) I:=[1, 4, 10, 20, 35]; [n le 5 select I[n] else 4*Self(n-1) - 6*Self(n-2) + 4*Self(n-3) - Self(n-4) + Self(n-5): n in [1..40]]; // _Vincenzo Librandi_, Jan 16 2026

%Y Cf. A000749, A369794, A390045.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jan 15 2026