A348310 - OEIS

%I #19 Oct 21 2022 21:24:19

%S 1,1,1,1,1,1,1,1,1,1,0,-5,-20,-55,-125,-251,-461,-791,-1286,-2001,

%T -3001,-4356,-6121,-8281,-10626,-12500,-12340,-6885,10110,49875,

%U 131626,286921,565781,1044971,1838626,3110751,5087561,8064366,12395461,18444251,26451625,36249035,46692715,54618710

%N a(n) = Sum_{k=0..floor(n/10)} (-1)^k * binomial(n-5*k,5*k).

%H Seiichi Manyama, <a href="/A348310/b348310.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1,0,0,0,0,-1).

%F G.f.: (1-x)^4/((1-x)^5 + x^10).

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

%t LinearRecurrence[{5, -10, 10, -5, 1, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 45] (* _Amiram Eldar_, Oct 11 2021 *)

%o (PARI) a(n) = sum(k=0, n\10, (-1)^k*binomial(n-5*k, 5*k));

%o (PARI) my(N=66, x='x+O('x^N)); Vec((1-x)^4/((1-x)^5+x^10))

%Y Cf. A348308, A348309.

%Y Cf. A289306, A348290.

%K sign,easy

%O 0,12

%A _Seiichi Manyama_, Oct 11 2021