A101563 - OEIS

%I #13 Aug 31 2024 18:07:18

%S 1,9,101,1009,10001,99909,1000001,10001009,100000101,999990009,

%T 10000000001,100000100909,1000000000001,9999999000009,100000000010101,

%U 1000000010001009,10000000000000001,99999999900099909

%N a(n) = (-1)^n * coefficient of x^n in Sum_{k>=1} x^(k-1)/(1+10*x^k).

%H G. C. Greubel, <a href="/A101563/b101563.txt">Table of n, a(n) for n = 0..990</a>

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * (10)^k * A051731(n+1, k+1).

%F a(n) = (-1)^n * Sum_{d|n+1} (-10)^(d-1). - _G. C. Greubel_, Jun 25 2024

%t A101563[n_]:= (-1)^n*DivisorSum[n+1, (-10)^(#-1) &];

%t Table[A101563[n], {n,0,40}] (* _G. C. Greubel_, Jun 25 2024 *)

%o (Magma)

%o A101563:= func< n | (&+[(-1)^(n-k)*(10)^k*0^((n+1) mod (k+1)): k in [0..n]]) >;

%o [A101563(n): n in [0..40]]; // _G. C. Greubel_, Jun 25 2024

%o (SageMath)

%o def A101563(n): return sum((-1)^(n+k)*(10)^k*0^((n+1)%(k+1)) for k in range(n+1))

%o [A101563(n) for n in range(41)] # _G. C. Greubel_, Jun 25 2024

%Y Cf. A051731, A081295, A048272, A101561, A101562.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Dec 07 2004