A060136 -id:A060136 - cp's OEIS frontend

A060137 Square array read by antidiagonals with T(n,k)=T(n,k-1)^2-n*T(n,k-1)+1 and T(n,0)=0.

0, 1, 0, 2, 1, 0, 5, 1, 1, 0, 26, 1, 0, 1, 0, 677, 1, 1, -1, 1, 0, 458330, 1, 0, 5, -2, 1, 0, 210066388901, 1, 1, 11, 13, -3, 1, 0, 44127887745906175987802, 1, 0, 89, 118, 25, -4, 1, 0, 1947270476915296449559703445493848930452791205, 1, 1, 7655, 13453, 501, 41, -5, 1, 0

Offset: 0

Henry Bottomley, Mar 05 2001

Index entries for sequences of form a(n+1)=a(n)^2 + ...

Rows include A003095, A057427, A000035. Columns include A000004, A000012, A022958, A001844 (offset). Cf. A060136.

T(0,k)=A004019(k-1)+1=A056207(k-2)+2. - R. J. Mathar, Apr 24 2007

A065035 a(n+1) = a(n)^2 + 3*a(n) + 1.

Original entry on oeis.org

0, 1, 5, 41, 1805, 3263441, 10650056950805, 113423713055421844361000441, 12864938683278671740537145998360961546653259485195805, 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185441

Offset: 0

Henry Bottomley, Nov 03 2001

a(k) is the optimal competitive ratio of any memoryless algorithm for the weighted k-server problem (Chiplunkar and Vishwanathan). - David Eppstein, Dec 31 2013

This is a divisibility sequence, that is if n divides m then a(n) divides a(m). Cf. A002065. - Peter Bala, Mar 26 2018

			a(3) = a(2)^2 + 3*a(2) + 1 = 25 + 15 + 1 = 41.

Harry J. Smith, Table of n, a(n) for n = 0..12
Ashish Chiplunkar and Sundar Vishwanathan, On Randomized Memoryless Algorithms for the Weighted k-server Problem, 54th IEEE Symp. Foundations of Computer Science (FOCS 2013), pp. 11-19; arXiv:1301.0123
Index entries for sequences of form a(n+1)=a(n)^2 + ...

Cf. A000058, A002065, A007018, A028387, A060136.

PARI
```
a(n)=if(n<1,0,a(n-1)^2+3*a(n-1)+1);
```

{ for (n=0, 12, a=if(n, a^2 + 3*a + 1, 0); write("b065035.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 03 2009

a(n) = A007018(n)-1 = A000058(n)-2 = A060136(3, n) = A028387(a(n-1)). - Michael Somos, Feb 10 2002

cp's OEIS Frontend

A060137 Square array read by antidiagonals with T(n,k)=T(n,k-1)^2-n*T(n,k-1)+1 and T(n,0)=0.

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A065035 a(n+1) = a(n)^2 + 3*a(n) + 1.

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