A080260 a(n)=1+(1/12)(n*(n+1)*(n+3)*(4-n)).

1, 3, 6, 7, 1, -19, -62, -139, -263, -449, -714, -1077, -1559, -2183, -2974, -3959, -5167, -6629, -8378, -10449, -12879, -15707, -18974, -22723, -26999, -31849, -37322, -43469, -50343, -57999, -66494, -75887, -86239, -97613, -110074, -123689, -138527, -154659, -172158, -191099, -211559

Offset

0,2

Comments

a(n) is the determinant of the n X n matrix M with m(i,i)=2i+1, m(i,j)=i+j.

Links

Table of n, a(n) for n=0..40.

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

Formula

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

a(n) = A002378(n) - A002415(n) + 1.

a(0)=1, a(1)=3, a(2)=6, a(3)=7, a(4)=1, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Sep 20 2014

Mathematica

Table[1+(n(n+1)(n+3)(4-n))/12, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 3, 6, 7, 1}, 50] (* Harvey P. Dale, Sep 20 2014 *)

Prog

(PARI) a(n) = 1+(1/12)*(n*(n+1)*(n+3)*(4-n)) \\ Michel Marcus, Jul 16 2013

Crossrefs

Sequence in context: A133340 A133329 A275696 * A065269 A137427 A177035

Adjacent sequences: A080257 A080258 A080259 * A080261 A080262 A080263

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Feb 11 2003

Extensions

Definition corrected by Michel Marcus, Jul 16 2013

Status

approved