A079903 a(n) = (9n^4 - 18n^3 + 18n^2 - 9n + 2)/2.

1, 28, 190, 703, 1891, 4186, 8128, 14365, 23653, 36856, 54946, 79003, 110215, 149878, 199396, 260281, 334153, 422740, 527878, 651511, 795691, 962578, 1154440, 1373653, 1622701, 1904176, 2220778, 2575315, 2970703, 3409966, 3896236, 4432753, 5022865

Offset: 1

Author

N. J. A. Sloane, Feb 21 2003

Keywords

• nonn
• easy

References

• E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982; p. 810.

Links

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

Programs

Magma

[(9*n^4 - 18*n^3 + 18*n^2 - 9*n + 2)/2 : n in [1..40]]; // Wesley Ivan Hurt, Jan 27 2017

Mathematica

Table[(9n^4 + 18n^2 + 5)/32, {n, 1, 71, 2}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 28, 190, 703, 1891}, 36] (* Harvey P. Dale, Jun 10 2011 *)

PARI

a(n)=(((9*n-18)*n+18)*n-9)*n/2+1 \\ Charles R Greathouse IV, Jun 10 2011

Formula

From Harvey P. Dale, Jun 10 2011: (Start)

G.f.: (x*(x*(x+3)*(x+20)+23)+1)/(1-x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), a(0) = 1, a(1) = 28, a(2) = 190, a(3) = 703, a(4) = 1891. (End)

a(n) = (3*n^2 - 3*n + 1)*(3*n^2 - 3*n + 2)/2. - Bruno Berselli, Jan 28 2017