A030441 Values of Newton-Gregory forward interpolating polynomial (1/3)*(2*n - 3)*(2*n^2 - 3*n + 4).

-4, -1, 2, 13, 40, 91, 174, 297, 468, 695, 986, 1349, 1792, 2323, 2950, 3681, 4524, 5487, 6578, 7805, 9176, 10699, 12382, 14233, 16260, 18471, 20874, 23477, 26288, 29315, 32566, 36049, 39772, 43743, 47970, 52461, 57224, 62267, 67598, 73225, 79156, 85399

Offset: 0

Author

Ilias.Kotsireas(AT)lip6.fr (Ilias Kotsireas)

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Equals A030434 shifted left twice.

Programs

Mathematica

LinearRecurrence[{4,-6,4,-1},{-4,-1,2,13},50] (* Harvey P. Dale, Apr 20 2015 *)

PARI

a(n) = (1/3)*(2*n-3)*(2*n^2-3*n+4); \\ Michel Marcus, May 18 2014

Formula

a(n) - A177342(n-1) = (n-1)^2, with n>1. For n=6, a(6) - A177342(5) = 174 - 149 = 5^2. - Bruno Berselli, May 23 2010

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Colin Barker, May 18 2014

G.f.: (15*x^3-18*x^2+15*x-4) / (x-1)^4. - Colin Barker, May 18 2014

a(n) = A059259(2*n,3), n>1. - Mathew Englander, May 17 2014