A165563 a(n) = 1 + 2*n + n^2 + 2*n^3 + n^4.

1, 7, 41, 151, 409, 911, 1777, 3151, 5201, 8119, 12121, 17447, 24361, 33151, 44129, 57631, 74017, 93671, 117001, 144439, 176441, 213487, 256081, 304751, 360049, 422551, 492857, 571591, 659401, 756959, 864961, 984127, 1115201, 1258951, 1416169, 1587671

Offset: 0

Author

Paul Curtz, Sep 22 2009

Keywords

• nonn
• easy

Comments

Also binomial transform of the quasi-finite sequence 1,6,28,48,24,0 (0 continued).

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)

Programs

Magma

[1 +2*n +n^2 +2*n^3 +n^4: n in [0..40] ]; // Vincenzo Librandi, Aug 06 2011

Mathematica

Table[1+2n+n^2+2n^3+n^4,{n,0,50}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,7,41,151,409},50] (* Harvey P. Dale, Nov 13 2021 *)

PARI

a(n)=1+2*n+n^2+2*n^3+n^4 \\ Charles R Greathouse IV, Oct 16 2015

Formula

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

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 24 -> 4th differences are 24 = A010863(n).

G.f.: (-1 - 2*x - 16*x^2 - 6*x^3 + x^4)/(x-1)^5.

Extensions

Edited and extended by R. J. Mathar, Sep 25 2009