OFFSET
0,1
COMMENTS
(1+sqrt(n))^5 = (5*n^2 + 10*n + 1) + (n^2 + 10*n + 5)*sqrt(n). For coefficients of the rational part see A134593.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = ((1+sqrt(n))^5 - (5*n^2 + 10*n + 1))/sqrt(n), for n > 0. [corrected by Jon E. Schoenfield, Nov 23 2018]
G.f.: (1+x)*(5-4*x)/(1-x)^3. - R. J. Mathar, Nov 14 2007
a(n) = 2*n + a(n-1) + 9 (with a(0)=5). - Vincenzo Librandi, Nov 23 2010
E.g.f.: (5 +11*x +x^2)*exp(x). - G. C. Greubel, Nov 23 2018
MATHEMATICA
Table[(n^2 + 10n + 5), {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {5, 16, 29}, 50] (* G. C. Greubel, Nov 23 2018 *)
PROG
(PARI) a(n)=n^2+10*n+5 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [n^2 +10*n +5: n in [0..50]]; // G. C. Greubel, Nov 23 2018
(Sage) [n^2 +10*n +5 for n in range(50)] # G. C. Greubel, Nov 23 2018
(GAP) List([0..50], n->n^2+10*n+5); # Muniru A Asiru, Nov 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Nov 04 2007
STATUS
approved