A072025 a(n) = n^4 + 2*n^3 + 4*n^2 + 3*n + 1 = ((n+1)^5+n^5) / (2*n+1).

1, 11, 55, 181, 461, 991, 1891, 3305, 5401, 8371, 12431, 17821, 24805, 33671, 44731, 58321, 74801, 94555, 117991, 145541, 177661, 214831, 257555, 306361, 361801, 424451, 494911, 573805, 661781, 759511, 867691, 987041, 1118305, 1262251, 1419671, 1591381

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

From Colin Barker, Dec 01 2015: (Start)

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.

G.f.: (1+x)^2*(1+4*x+x^2) / (1-x)^5.

(End)

Mathematica

Table[((n+1)^5+n^5)/(2n+1), {n, 0, 30}] (* Vincenzo Librandi, Nov 23 2011 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 11, 55, 181, 461}, 50] (* Harvey P. Dale, Dec 14 2019 *)

Prog

(Magma) [((n+1)^5+n^5)/(2*n+1): n in [0..40]]; // Vincenzo Librandi, Nov 23 2011
(PARI) a(n)=n^4+2*n^3+4*n^2+3*n+1 \\ Charles R Greathouse IV, Nov 23 2011
(PARI) Vec((1+x)^2*(1+4*x+x^2)/(1-x)^5 + O(x^100)) \\ Colin Barker, Dec 01 2015

Crossrefs

Cf. A022521, A072024.

Sequence in context: A009550 A226255 A022606 * A098992 A246990 A156589

Adjacent sequences: A072022 A072023 A072024 * A072026 A072027 A072028

Keyword

nonn,easy,less

Author

Henry Bottomley, Jun 06 2002

Status

approved