A057651 -id:A057651 - cp's OEIS frontend

A198768 a(n) = 9*5^n-1.

8, 44, 224, 1124, 5624, 28124, 140624, 703124, 3515624, 17578124, 87890624, 439453124, 2197265624, 10986328124, 54931640624, 274658203124, 1373291015624, 6866455078124, 34332275390624, 171661376953124, 858306884765624

Offset: 0

Vincenzo Librandi, Oct 30 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-5).

Cf. A024049, A057651, A081655.

Magma
```
[9*5^n-1: n in [0..30]];
```

9 5^Range[0, 20] - 1 (* or *) LinearRecurrence[{6, -5}, {8, 44}, 20] (* Harvey P. Dale, Nov 01 2011 *)
CoefficientList[Series[(8 - 4 x)/(1 - 6 x + 5 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 03 2013 *)

a(n) = 5*a(n-1)+4.
a(n) = 6*a(n-1)-5*a(n-2), n > 1.
G.f.: (8 - 4*x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 03 2013

A198769 a(n) = (9*5^n-1)/4.

Original entry on oeis.org

2, 11, 56, 281, 1406, 7031, 35156, 175781, 878906, 4394531, 21972656, 109863281, 549316406, 2746582031, 13732910156, 68664550781, 343322753906, 1716613769531, 8583068847656, 42915344238281, 214576721191406, 1072883605957031, 5364418029785156, 26822090148925781

Offset: 0

Vincenzo Librandi, Oct 30 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-5).

Cf. A024049, A057651, A081655.

Magma
```
[(9*5^n-1)/4: n in [0..30]];
```

(9*5^Range[0,30]-1)/4 (* or *) LinearRecurrence[{6,-5},{2,11},30] (* Harvey P. Dale, May 07 2012 *)

a(n) = 5*a(n-1)+1.
a(n) = 6*a(n-1)-5*a(n-2), n>1.
G.f.: (2-x)/(5*x^2-6*x+1). - Harvey P. Dale, May 07 2012

A198770 11*5^n-1.

Original entry on oeis.org

10, 54, 274, 1374, 6874, 34374, 171874, 859374, 4296874, 21484374, 107421874, 537109374, 2685546874, 13427734374, 67138671874, 335693359374, 1678466796874, 8392333984374, 41961669921874, 209808349609374, 1049041748046874

Offset: 0

Vincenzo Librandi, Oct 30 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-5).

Cf. A024049, A057651, A081655.

Magma
```
[11*5^n-1: n in [0..30]];
```

CoefficientList[Series[2*(5 - 3*x)/(1 - 6*x + 5*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
11*5^Range[0,20]-1 (* or *) LinearRecurrence[{6,-5},{10,54},30] (* Harvey P. Dale, May 14 2019 *)

a(n) = 5*a(n-1)+4.
a(n)= = 6*a(n-1)-5*a(n-2), n>1.
G.f.: 2*(5 - 3*x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 04 2013

A067763 Square array read by antidiagonals of base n numbers written as 122...222 with k 2's (and a suitable interpretation for n=0, 1 or 2).

Original entry on oeis.org

1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 7, 10, 5, 1, 2, 9, 22, 17, 6, 1, 2, 11, 46, 53, 26, 7, 1, 2, 13, 94, 161, 106, 37, 8, 1, 2, 15, 190, 485, 426, 187, 50, 9, 1, 2, 17, 382, 1457, 1706, 937, 302, 65, 10, 1, 2, 19, 766, 4373, 6826, 4687, 1814, 457, 82, 11, 1, 2, 21, 1534, 13121

Offset: 0

Henry Bottomley, Feb 06 2002

Start with a node; step one is to connect that node to n+1 new nodes so that it is of degree n+1; further steps are to connect each existing node of degree 1 to n new nodes so that it is of degree n+1; T(n,k) is the total number of nodes after k steps.

			Rows start: 1,2,2,2,2,2,...; 1,3,5,7,9,11,...; 1,4,10,22,46,94,...; 1,5,17,53,161,485,... T(3,2) =122 base 3 =17.

Rows include A040000, A005408, A033484, A048473, A020989, A057651, A061801 etc. For negative n (not shown) absolute values of rows would effectively include A000012, A014113, A046717.

T(n, k) =((n+1)*n^k-2)/(n-1) [with T(1, k)=2k+1] =n*T(n, k-1)+2 =(n+1)*T(n, k-1)-n*T(n, k-2) =T(n, k-1)+(1+1/n)*n^k =A055129(k, n)+A055129(k-1, n). Coefficient of x^k in expansion of (1+x)/((1-x)(1-nx)).

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A198768 a(n) = 9*5^n-1.

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A198769 a(n) = (9*5^n-1)/4.

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A198770 11*5^n-1.

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A067763 Square array read by antidiagonals of base n numbers written as 122...222 with k 2's (and a suitable interpretation for n=0, 1 or 2).

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