

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
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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(n1) a(n2), n>3.  R. J. Mathar, Apr 21 2010, corrected Sep 02 2010
G.f.: (1 + 2*x^2 + 2*x^3)/(1x)^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*(n1), {n, 2, 25}]] (* G. C. Greubel, Sep 18 2016 *)


PROG

(MAGMA) [1, 2] cat [5*(n1): 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 by 65  R. J. Mathar, Apr 21 2010


STATUS

approved



