OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (-1,2,2,-1,-1).
FORMULA
a(n) = n*S(n) - n + Sum_{k=1..n} S(k) where S(n) = (-1)^(n-1)*n.
From Andrew Howroyd, Aug 28 2018: (Start)
a(n) = (-1)^(n-1)*(n^2 + ceiling(n/2)) - n.
a(n) = -a(n-1) + 2*a(n-2) + 2*a(n-3) - a(n-4) - a(n-5) for n > 5.
G.f.: x*(1 - 6*x - x^2 - 2*x^3)/((1 - x)^2*(1 + x)^3).
(End)
EXAMPLE
a(4) = 22 = sum of row 4 terms of triangle A132898: (-4, -7, -2, -9).
a(4) = 22 = n*S(n) - n + SUM_{1,n}:S(n) = 4*(-4) - 4 + (1, -2, 3, -4) = -16 - 4 - 2.
MATHEMATICA
LinearRecurrence[{-1, 2, 2, -1, -1}, {1, -7, 8, -22, 23}, 50] (* Stefano Spezia, Sep 01 2018 *)
PROG
(PARI) a(n)={(-1)^(n-1)*(n^2 + ceil(n/2)) - n} \\ Andrew Howroyd, Aug 28 2018
(PARI) Vec((1 - 6*x - x^2 - 2*x^3)/((1 - x)^2*(1 + x)^3) + O(x^50)) \\ Andrew Howroyd, Aug 28 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Gary W. Adamson, Sep 03 2007
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Aug 28 2018
STATUS
approved