A156677 -id:A156677 - cp's OEIS frontend

A017305 a(n) = 10*n + 3.

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, 123, 133, 143, 153, 163, 173, 183, 193, 203, 213, 223, 233, 243, 253, 263, 273, 283, 293, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 403, 413, 423, 433, 443, 453, 463, 473, 483, 493, 503, 513, 523, 533

Offset: 0

N. J. A. Sloane

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0(38).

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Tanya Khovanova, Recursive Sequences.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008592, A016885, A017198, A017281, A017293, A156677.

[10*n+3: n in [0..60]]; // Vincenzo Librandi, May 28 2011

Range[3, 1000, 10] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)

a(n) = A017198(n) - A156677(n+2). - Reinhard Zumkeller, Jul 13 2010
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, May 28 2011
G.f.: (3+7*x)/(x-1)^2. - R. J. Mathar, Apr 11 2016
E.g.f.: exp(x)*(3 + 10*x). - Stefano Spezia, Aug 22 2023
a(n) = A016885(2*n). - Elmo R. Oliveira, Apr 10 2025

A017198 a(n) = (9*n + 3)^2.

Original entry on oeis.org

9, 144, 441, 900, 1521, 2304, 3249, 4356, 5625, 7056, 8649, 10404, 12321, 14400, 16641, 19044, 21609, 24336, 27225, 30276, 33489, 36864, 40401, 44100, 47961, 51984, 56169, 60516, 65025, 69696

Offset: 0

N. J. A. Sloane

a(n) = A000290(A017197(n)) = A156677(n+2) + A017305(n). - Reinhard Zumkeller, Jul 13 2010

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

[(9*n+3)^2: n in [0..35]]; // Vincenzo Librandi, Jul 23 2011

(9*Range[0, 30] + 3)^2 (* or *) LinearRecurrence[{3,-3,1},{9,144,441},30] (* Harvey P. Dale, Dec 25 2015 *)

a(n)=(9*n+3)^2 \\ Charles R Greathouse IV, Jun 17 2017

a(0)=9, a(1)=144, a(2)=441, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Dec 25 2015

G.f.: (-9 - 117*x - 36*x^2) / (x-1)^3. - R. J. Mathar, Jul 14 2016

A156771 a(n) = 729*n - 531.

Original entry on oeis.org

198, 927, 1656, 2385, 3114, 3843, 4572, 5301, 6030, 6759, 7488, 8217, 8946, 9675, 10404, 11133, 11862, 12591, 13320, 14049, 14778, 15507, 16236, 16965, 17694, 18423, 19152, 19881, 20610, 21339, 22068, 22797, 23526, 24255, 24984, 25713

Offset: 1

Vincenzo Librandi, Feb 15 2009

The identity (6561*n^2 - 9558*n + 3482)^2 - (81*n^2 - 118*n + 43)*(729*n - 531)^2 = 1 can be written as A156773(n)^2 - A156677(n)*a(n)^2 = 1.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A156677, A156773.

I:=[198, 927]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

Mathematica
```
LinearRecurrence[{2,-1},{198,927},40]
```

a(n)=729*n-531 \\ Charles R Greathouse IV, Dec 23 2011

[9*(81*n -59) for n in [1..50]] # G. C. Greubel, Jun 19 2021

a(n) = 2*a(n-1) - a(n-2).
G.f.: x*(198 + 531*x)/(1-x)^2.
E.g.f.: 9*(59 - (59 - 81*x)*exp(x)). - G. C. Greubel, Jun 19 2021

A156773 a(n) = 6561n^2 - 9558n + 3482.

Original entry on oeis.org

3482, 485, 10610, 33857, 70226, 119717, 182330, 258065, 346922, 448901, 564002, 692225, 833570, 988037, 1155626, 1336337, 1530170, 1737125, 1957202, 2190401, 2436722, 2696165, 2968730, 3254417, 3553226, 3865157, 4190210, 4528385

Offset: 0

Vincenzo Librandi, Feb 15 2009

The identity (6561*n^2 - 9558*n + 3482)^2 - (81*n^2 - 118*n + 43)*(729*n - 531)^2 = 1 can be written as a(n)^2 - A156677(n)*A156771(n)^2 = 1 for n>0. [rewritten by Bruno Berselli, Jul 21 2011]

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A156677, A156771.

Magma
```
[6561*n^2-9558*n+3482: n in [0..35]];
```

Table[6561n^2-9558n+3482,{n,0,30}] (* Harvey P. Dale, Apr 06 2011 *)

a(n)=6561*n^2-9558*n+3482 \\ Charles R Greathouse IV, Dec 23 2011

[3482 -9558*n +6561*n^2 for n in (0..35)] # G. C. Greubel, Jun 21 2021

G.f.: (3482 - 9961*x + 19601*x^2)/(1-x)^3. - Colin Barker, Jan 09 2012
E.g.f.: (3482 - 2997*x + 6561*x^2)*exp(x). - G. C. Greubel, Jun 21 2021
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, Sep 03 2022

Checked by Michael B. Porter, Jun 16 2010

Offset corrected by N. J. A. Sloane, Jun 22 2010

cp's OEIS Frontend

A017305 a(n) = 10*n + 3.

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A017198 a(n) = (9*n + 3)^2.

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A156771 a(n) = 729*n - 531.

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Formula

A156773 a(n) = 6561*n^2 - 9558*n + 3482.

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Author

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Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Formula

Extensions

A156773 a(n) = 6561n^2 - 9558n + 3482.