A369839 - OEIS

%I #17 Mar 15 2024 11:08:34

%S 1,3,11,45,185,756,3084,12580,51320,209365,854126,3484490,14215310,

%T 57992715,236586825,965178576,3937538296,16063564001,65532845396,

%U 267347509271,1090669728772,4449491452173,18152125855049,74053333195325,302107654008601,1232477063116753

%N Number of compositions of 5*n-4 into parts 1 and 5.

%H Paolo Xausa, <a href="/A369839/b369839.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,10,-5,1).

%F a(n) = A003520(5*n-4).

%F a(n) = Sum_{k=0..n} binomial(n+4*k,n-1-k).

%F a(n) = 6*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

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

%t LinearRecurrence[{6, -10, 10, -5, 1}, {1, 3, 11, 45, 185}, 50] (* _Paolo Xausa_, Mar 15 2024 *)

%o (PARI) a(n) = sum(k=0, n, binomial(n+4*k, n-1-k));

%Y Cf. A079675, A369836, A369837, A369838.

%Y Cf. A003520.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Feb 03 2024