A017557 a(n) = 12*n + 3.
3, 15, 27, 39, 51, 63, 75, 87, 99, 111, 123, 135, 147, 159, 171, 183, 195, 207, 219, 231, 243, 255, 267, 279, 291, 303, 315, 327, 339, 351, 363, 375, 387, 399, 411, 423, 435, 447, 459, 471, 483, 495, 507, 519, 531, 543, 555, 567, 579, 591, 603, 615, 627, 639
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
- 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).
Programs
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GAP
List([0..60], n-> 12*n+3 ); # G. C. Greubel, Sep 18 2019
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Haskell
a017557 = (+ 3) . (* 12) -- Reinhard Zumkeller, Jul 05 2013
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Magma
[12*n+3: n in [0..60]]; // Vincenzo Librandi, Jun 07 2011
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Maple
seq(12*n+3, n=0..60); # G. C. Greubel, Sep 18 2019
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Mathematica
12*Range[0,60]+3 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)
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PARI
a(n)=12*n+3 \\ Charles R Greathouse IV, Jul 10 2016
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Sage
[12*n+3 for n in (0..60)] # G. C. Greubel, Sep 18 2019
Formula
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 07 2011
A089911(2*a(n)) = 8. - Reinhard Zumkeller, Jul 05 2013
From G. C. Greubel, Sep 18 2019: (Start)
G.f.: 3*(1+3*x)/(1-x)^2.
E.g.f.: 3*(1+4*x)*exp(x). (End)
Sum_{n>=0} (-1)^n/a(n) = (Pi + 2*log(sqrt(2)+1))/(12*sqrt(2)). - Amiram Eldar, Dec 12 2021
Comments