

A134594


a(n) = n^2 + 10*n + 5: coefficients of the irrational part of (1 + sqrt(n))^5.


2



5, 16, 29, 44, 61, 80, 101, 124, 149, 176, 205, 236, 269, 304, 341, 380, 421, 464, 509, 556, 605, 656, 709, 764, 821, 880, 941, 1004, 1069, 1136, 1205, 1276, 1349, 1424, 1501, 1580, 1661, 1744, 1829, 1916, 2005, 2096, 2189, 2284, 2381, 2480, 2581, 2684
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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)*(54*x)/(1x)^3.  R. J. Mathar, Nov 14 2007
a(n) = 2*n + a(n1) + 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

Cf. A134593.
Sequence in context: A063290 A299882 A212457 * A222535 A063076 A270805
Adjacent sequences: A134591 A134592 A134593 * A134595 A134596 A134597


KEYWORD

nonn,easy


AUTHOR

Artur Jasinski, Nov 04 2007


STATUS

approved



