A177059 a(n) = 25*n^2 + 25*n + 6.
6, 56, 156, 306, 506, 756, 1056, 1406, 1806, 2256, 2756, 3306, 3906, 4556, 5256, 6006, 6806, 7656, 8556, 9506, 10506, 11556, 12656, 13806, 15006, 16256, 17556, 18906, 20306, 21756, 23256, 24806, 26406, 28056, 29756, 31506, 33306, 35156, 37056, 39006, 41006, 43056
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Programs
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Magma
I:=[6, 56, 156]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 03 2012
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Mathematica
LinearRecurrence[{3, -3, 1}, {6, 56, 156}, 50] (* Vincenzo Librandi, Feb 03 2012 *) Table[25n^2+25n+6,{n,0,40}] (* Harvey P. Dale, Mar 30 2019 *) -
PARI
a(n)=25*n^2+25*n+6 \\ Charles R Greathouse IV, Dec 28 2011
Formula
a(n) = (5*n + 2)*(5*n + 3).
a(n) = 50*n + a(n-1) with a(0)=6.
a(n) = 25*A002061(n+1) - 19. - Reinhard Zumkeller, Jun 16 2010
G.f.: (6 + 38*x + 6*x^2)/(1-x)^3. - Vincenzo Librandi, Feb 03 2012
From Amiram Eldar, Jan 23 2022: (Start)
Sum_{n>=0} 1/a(n) = sqrt(1 - 2/sqrt(5))*Pi/5.
Sum_{n>=0} (-1)^n/a(n) = 2*log(phi)/sqrt(5) - 2*log(2)/5, where phi is the golden ratio (A001622).
Product_{n>=0} (1 - 1/a(n)) = 2*sqrt(2/(5+sqrt(5))) * cos(Pi/(2*sqrt(5))).
Product_{n>=0} (1 + 1/a(n)) = sqrt(2 - 2/sqrt(5)) * cosh(sqrt(3)*Pi/10).
Product_{n>=0} (1 - 2/a(n)) = 1/phi. (End)
From Elmo R. Oliveira, Oct 24 2024: (Start)
E.g.f.: exp(x)*(6 + 25*x*(2 + x)).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
Comments