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A132899 Row sums of triangle A132898. 2
1, -7, 8, -22, 23, -45, 46, -76, 77, -115, 116, -162, 163, -217, 218, -280, 281, -351, 352, -430, 431, -517, 518, -612, 613, -715, 716, -826, 827, -945, 946, -1072, 1073, -1207, 1208, -1350, 1351, -1501, 1502, -1660, 1661, -1827, 1828, -2002, 2003, -2185, 2186 (list; graph; refs; listen; history; text; internal format)
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

Cf. A132898.

Sequence in context: A152043 A181585 A060291 * A051175 A322651 A325322

Adjacent sequences:  A132896 A132897 A132898 * A132900 A132901 A132902

KEYWORD

sign

AUTHOR

Gary W. Adamson, Sep 03 2007

EXTENSIONS

Terms a(11) and beyond from Andrew Howroyd, Aug 28 2018

STATUS

approved

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Last modified September 28 21:46 EDT 2020. Contains 337414 sequences. (Running on oeis4.)