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A143208 a(1)=2; for n>1, a(n) = (4-9*n+3*n^2)/2. 1
2, -1, 2, 8, 17, 29, 44, 62, 83, 107, 134, 164, 197, 233, 272, 314, 359, 407, 458, 512, 569, 629, 692, 758, 827, 899, 974, 1052, 1133, 1217, 1304, 1394, 1487, 1583, 1682, 1784, 1889, 1997, 2108, 2222, 2339, 2459, 2582, 2708, 2837, 2969, 3104, 3242, 3383, 3527, 3674 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Old Name was: A sequence based on odd numbers of the type 3*n + 2: a(n) = a(n - 1) + n - 1; A000096; f(n) = 3*a(n)+2.

LINKS

Table of n, a(n) for n=1..51.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

From Colin Barker, Apr 14 2014: (Start)

a(n) = (4-9*n+3*n^2)/2 for n>1.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4.

G.f.: x*(3*x^3-11*x^2+7*x-2) / (x-1)^3. (End).

a(n) = (n-2)*A095794(n) - (n-1)*A095794(n-1) for n>1. [Bruno Berselli, May 19 2015]

EXAMPLE

G.f. = 2*x - x^2 + 2*x^3 + 8*x^4 + 17*x^5 + 29*x^6 + 44*x^7 + 62*x^8 + ...

MATHEMATICA

a[0] = 0; a[1] = -1; a[n_] := a[n] = a[n - 1] + n - 1; a1 = Table[a[n], {n, 0, 30}]; f[n_] := 3*a[n] + 2; Table[f[n], {n, 0, 50}]

LinearRecurrence[{3, -3, 1}, {2, -1, 2, 8}, 60] (* Harvey P. Dale, Mar 22 2018 *)

PROG

(PARI) Vec(x*(3*x^3-11*x^2+7*x-2)/(x-1)^3 + O(x^100)) \\ Colin Barker, Apr 14 2014

CROSSREFS

Cf. A095794.

Sequence in context: A137305 A282885 A242841 * A188664 A326572 A119419

Adjacent sequences:  A143205 A143206 A143207 * A143209 A143210 A143211

KEYWORD

sign,easy

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 20 2008

EXTENSIONS

Better name and edits by Colin Barker and Joerg Arndt, Apr 14 2014

STATUS

approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)