A166526 -id:A166526 - cp's OEIS frontend

A166525 a(n) = 10*n - a(n-1), with n>1, a(1)=1.

1, 19, 11, 29, 21, 39, 31, 49, 41, 59, 51, 69, 61, 79, 71, 89, 81, 99, 91, 109, 101, 119, 111, 129, 121, 139, 131, 149, 141, 159, 151, 169, 161, 179, 171, 189, 181, 199, 191, 209, 201, 219, 211, 229, 221, 239, 231, 249, 241, 259, 251, 269, 261, 279, 271, 289

Offset: 1

Vincenzo Librandi, Oct 16 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A166519, A166520, A166521, A166522, A166523, A166524, A166526.

[n eq 1 select 1 else 10*n-Self(n-1): n in [1..80]]; // Vincenzo Librandi, Sep 13 2013

CoefficientList[Series[(1 +18 x -9 x^2)/((1+x) (1-x)^2), {x,0,80}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{1,1,-1}, {1,19,11}, 50] (* G. C. Greubel, May 16 2016 *)

def A166525(n): return 5*n - 4 + 13*((n+1)%2)
[A166525(n) for n in range(1, 101)] # G. C. Greubel, Aug 04 2024

G.f.: x*(1+18*x-9*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Mar 08 2011
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: (1/2)*(13*exp(-x) + 5*(1 + 2*x)*exp(x) - 18).
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/9 + sqrt(5+2*sqrt(5))*Pi/10. - Amiram Eldar, Feb 24 2023
a(n) = (1/2)*(10*n + 5 + 13*(-1)^n). - G. C. Greubel, Aug 04 2024

A166520 a(n) = (10n + 11(-1)^n + 5)/4.

Original entry on oeis.org

1, 9, 6, 14, 11, 19, 16, 24, 21, 29, 26, 34, 31, 39, 36, 44, 41, 49, 46, 54, 51, 59, 56, 64, 61, 69, 66, 74, 71, 79, 76, 84, 81, 89, 86, 94, 91, 99, 96, 104, 101, 109, 106, 114, 111, 119, 116, 124, 121, 129, 126, 134, 131, 139, 136, 144, 141, 149, 146, 154, 151, 159

Offset: 1

Vincenzo Librandi, Oct 16 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A166519, A166521, A166522, A166523, A166524, A166525, A166526.

[5*n/2 + 11*(-1)^n/4 +5/4: n in [1..80]]; // Vincenzo Librandi, Sep 13 2013

Table[5 n / 2 + 11 (-1)^n / 4 + 5 / 4, {n, 100}] (* Vincenzo Librandi, Sep 13 2013 *)

def A166520(n): return (5*n -3 +11*((n+1)%2))//2
[A166520(n) for n in range(1,101)] # G. C. Greubel, Aug 03 2024

a(n) = 5*n - a(n-1) for n > 1, with a(1) = 1.
G.f. x*(1+8*x-4*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Mar 08 2011
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: (5*(1 + 2*x)*exp(x) + 11*exp(-x) - 16)/4.
a(n) = a(n-1) + a(n-2) - a(n-3). (End)

A166521 a(n) = (6n + 7(-1)^n + 3)/2.

Original entry on oeis.org

1, 11, 7, 17, 13, 23, 19, 29, 25, 35, 31, 41, 37, 47, 43, 53, 49, 59, 55, 65, 61, 71, 67, 77, 73, 83, 79, 89, 85, 95, 91, 101, 97, 107, 103, 113, 109, 119, 115, 125, 121, 131, 127, 137, 133, 143, 139, 149, 145, 155, 151, 161, 157, 167, 163, 173, 169, 179, 175, 185

Offset: 1

Vincenzo Librandi, Oct 16 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A166519, A166520, A166522, A166523, A166524, A166525, A166526.

[(6*n+7*(-1)^n+3)/2: n in [1..80]]; // Vincenzo Librandi, Sep 13 2013

Table[(6 n + 7 (-1)^n + 3)/2, {n, 60}] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{1,1,-1},{1,11,7},90] (* Harvey P. Dale, Apr 29 2018 *)

def A166521(n): return 3*n -2 +7*((n+1)%2)
[A166521(n) for n in range(1,101)] # G. C. Greubel, Aug 03 2024

a(n) = 6*n - a(n-1), for n > 1, with a(1) = 1.
G.f.: x*(1+10*x-5*x^2) / ((1+x)*(1-x)^2). - R. J. Mathar, Mar 08 2011
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: (1/2)*(7*exp(-x) + 3*(1+2*x)*exp(x) -10).
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/5 + Pi/(2*sqrt(3)). - Amiram Eldar, Feb 24 2023

A166522 a(n) = 7*n - a(n-1), with a(1) = 1.

Original entry on oeis.org

1, 13, 8, 20, 15, 27, 22, 34, 29, 41, 36, 48, 43, 55, 50, 62, 57, 69, 64, 76, 71, 83, 78, 90, 85, 97, 92, 104, 99, 111, 106, 118, 113, 125, 120, 132, 127, 139, 134, 146, 141, 153, 148, 160, 155, 167, 162, 174, 169, 181, 176, 188, 183, 195, 190, 202, 197, 209, 204

Offset: 1

Vincenzo Librandi, Oct 16 2009

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A166519, A166520, A166521, A166523, A166524, A166525, A166526.

A166522:= func< n | ( 7*n -5 +17*((n+1) mod 2) )/2 >;
[A166522(n): n in [1..100]]; // G. C. Greubel, Aug 03 2024

RecurrenceTable[{a[1]==1,a[n]==7n-a[n-1]},a,{n,60}] (* or *) LinearRecurrence[{1,1,-1},{1,13,8},60] (* Harvey P. Dale, Jun 07 2012 *)

def A166522(n): return ( 7*n -5 +17*((n+1)%2) )//2
[A166522(n) for n in range(1,101)] # G. C. Greubel, Aug 03 2024

G.f.: x*(1+12*x-6*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Mar 08 2011
a(n) = a(n-1) + a(n-2) - a(n-3), a(1)=1, a(2)=13, a(3)=8. - Harvey P. Dale, Jun 07 2012
E.g.f.: (1/4)*(17*exp(-x) + 7*(1 + 2*x)*exp(x) - 24). - G. C. Greubel, May 16 2016
a(n) = (1/4)*(14*n + 7 + 17*(-1)^n). - G. C. Greubel, Aug 03 2024

A166523 a(n) = 8*n - a(n-1), with n>1, a(1)=1.

Original entry on oeis.org

1, 15, 9, 23, 17, 31, 25, 39, 33, 47, 41, 55, 49, 63, 57, 71, 65, 79, 73, 87, 81, 95, 89, 103, 97, 111, 105, 119, 113, 127, 121, 135, 129, 143, 137, 151, 145, 159, 153, 167, 161, 175, 169, 183, 177, 191, 185, 199, 193, 207, 201, 215, 209, 223, 217, 231, 225, 239, 233

Offset: 1

Vincenzo Librandi, Oct 16 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A166519, A166520, A166521, A166522, A166524, A166525, A166526.

[n eq 1 select 1 else 8*n-Self(n-1): n in [1..70]]; // Vincenzo Librandi, Sep 13 2013

CoefficientList[Series[(1 +14 x -7 x^2)/((1+x) (1-x)^2), {x,0,60}], x] (* Vincenzo Librandi, Sep 13 2013 *)

def A166523(n): return 4*n - 3 + 10*((n+1)%2)
[A166523(n) for n in range(1,101)] # G. C. Greubel, Aug 03 2024

G.f.: x*(1+14*x-7*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Mar 08 2011
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: 5*exp(-x) + 2*(1 + 2*x)*exp(x) - 7.
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/7 + (1/8 + 1/(4*sqrt(2)))*Pi. - Amiram Eldar, Feb 24 2023
a(n) = 4*n + 2 + 5*(-1)^n. - G. C. Greubel, Aug 03 2024

A166524 a(n) = 9*n - a(n-1), with n>1, a(1)=1.

Original entry on oeis.org

1, 17, 10, 26, 19, 35, 28, 44, 37, 53, 46, 62, 55, 71, 64, 80, 73, 89, 82, 98, 91, 107, 100, 116, 109, 125, 118, 134, 127, 143, 136, 152, 145, 161, 154, 170, 163, 179, 172, 188, 181, 197, 190, 206, 199, 215, 208, 224, 217, 233, 226, 242, 235, 251, 244, 260, 253

Offset: 1

Vincenzo Librandi, Oct 16 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A166519, A166520, A166521, A166522, A166523, A166525, A166526.

[n eq 1 select 1 else 9*n-Self(n-1): n in [1..80]]; // Vincenzo Librandi, Sep 13 2013

CoefficientList[Series[(1 +16 x -8 x^2)/((1+x) (1-x)^2), {x,0,80}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{1,1,-1},{1,17,10},60] (* Harvey P. Dale, Dec 24 2014 *)

def A166524(n): return (9*n - 7 + 23*((n+1)%2))//2
[A166524(n) for n in range(1, 101)] # G. C. Greubel, Aug 04 2024

G.f.: x*(1+16*x-8*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Mar 08 2011
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: (1/4)*(23*exp(-x) + 9*(1 + 2*x)*exp(x) - 32).
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/8 + cot(Pi/9)*Pi/9. - Amiram Eldar, Feb 24 2023
a(n) = (1/4)*(18*n + 9 + 23*(-1)^n). - G. C. Greubel, Aug 04 2024

A166539 a(n) = (10n + 7(-1)^n + 5)/4.

Original entry on oeis.org

2, 8, 7, 13, 12, 18, 17, 23, 22, 28, 27, 33, 32, 38, 37, 43, 42, 48, 47, 53, 52, 58, 57, 63, 62, 68, 67, 73, 72, 78, 77, 83, 82, 88, 87, 93, 92, 98, 97, 103, 102, 108, 107, 113, 112, 118, 117, 123, 122, 128, 127, 133, 132, 138, 137, 143, 142, 148, 147, 153, 152, 158

Offset: 1

Vincenzo Librandi, Oct 16 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A166519, A166520, A166521, A166522, A166523, A166524, A166525, A166526.

[5*n/2 + (5+7*(-1)^n)/4: n in [1..70]]; // Vincenzo Librandi, May 15 2013

RecurrenceTable[{a[1]==2,a[n]==5n-a[n-1]},a[n],{n,70}] (* or *) LinearRecurrence[{1,1,-1},{2,8,7},70] (* Harvey P. Dale, Jun 29 2011 *)

def A166539(n): return (5*n - 1 + 7*((n+1)%2))//2
[A166539(n) for n in range(1, 101)] # G. C. Greubel, Aug 04 2024

a(n) = 5*n - a(n-1), n>=2.
From Harvey P. Dale, Jun 29 2011: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3), n>=4.
G.f.: x*(2+3*x*(2-x))/((1-x)^2*(1+x)). (End)
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: (1/4)*(5*(1 + 2*x)*exp(x) + 7*exp(-x) - 12).
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/3 + sqrt((5-2*sqrt(5))/5)*Pi/5. - Amiram Eldar, Feb 24 2023
a(n) = A166520(n) - (-1)^n. - G. C. Greubel, Aug 04 2024

cp's OEIS Frontend

A166525 a(n) = 10*n - a(n-1), with n>1, a(1)=1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A166520 a(n) = (10*n + 11*(-1)^n + 5)/4.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A166521 a(n) = (6*n + 7*(-1)^n + 3)/2.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A166522 a(n) = 7*n - a(n-1), with a(1) = 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A166523 a(n) = 8*n - a(n-1), with n>1, a(1)=1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A166524 a(n) = 9*n - a(n-1), with n>1, a(1)=1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A166539 a(n) = (10*n + 7*(-1)^n + 5)/4.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A166520 a(n) = (10n + 11(-1)^n + 5)/4.

A166521 a(n) = (6n + 7(-1)^n + 3)/2.

A166539 a(n) = (10n + 7(-1)^n + 5)/4.