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A135042 Binomial transform of [1, 1, 2, 0, -2, 4, -6, 8, -10, 12, ...]. 2
1, 2, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A007318 * [1, 1, 2, 0, -2, 4, -6, 8, -10, 12, ...].

Sum of antidiagonal terms of the following arithmetic array:

  1, 1, 1,  1,  1, ...

  1, 3, 5,  7,  9, ...

  1, 4, 7, 10, 13, ...

  ...

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

a(n) = 2*a(n-1) - a(n-2), n > 3. - R. J. Mathar, Apr 21 2010, corrected Sep 02 2010

G.f.: (1 + 2*x^2 + 2*x^3)/(1-x)^2. - Colin Barker, Feb 01 2012

From G. C. Greubel, Sep 18 2016: (Start)

a(n) = 5*(n + 1) for n >= 3.

E.g.f.: 5*(-1 + x)*exp(x) + 2*(3 + x). (End)

EXAMPLE

a(4) = 10 = (1, 3, 3, 1) dot (1, 1, 2, 0) = (1 + 3 + 6 + 0).

a(4) = 10 = (4 + 5 + 1).

MATHEMATICA

Join[{1, 2}, Table[5*(n-1), {n, 2, 25}]] (* G. C. Greubel, Sep 18 2016 *)

PROG

(Magma) [1, 2] cat [5*(n-1): n in [2..50]]; // Vincenzo Librandi, Sep 18 2016

CROSSREFS

Sequence in context: A105370 A173694 A190459 * A109666 A215098 A024390

Adjacent sequences:  A135039 A135040 A135041 * A135043 A135044 A135045

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, May 10 2008

EXTENSIONS

Offset corrected, and one 75 replaced with 65, by R. J. Mathar, Apr 21 2010

STATUS

approved

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Last modified September 26 16:09 EDT 2022. Contains 357000 sequences. (Running on oeis4.)