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A140229 Binomial transform of [1, 3, 3, 1, -2, 3, -4, 5, ...]. 2
1, 4, 10, 20, 33, 49, 68, 90, 115, 143, 174, 208, 245, 285, 328, 374, 423, 475, 530, 588, 649, 713, 780, 850, 923, 999, 1078, 1160, 1245, 1333, 1424, 1518, 1615, 1715, 1818, 1924, 2033, 2145, 2260, 2378, 2499, 2623, 2750, 2880, 3013, 3149, 3288, 3430, 3575 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The falling diagonal starting with T(1,4) in A049777 (as a square array) gives the terms of this sequence for n >=3. - Bob Selcoe, Oct 27 2014

LINKS

Table of n, a(n) for n=1..49.

FORMULA

A007318 * [1, 3, 3, 1, -2, 3, -4, 5,...].

a(n) = (n+1)(3n-4)/2, for n>=3. - Emeric Deutsch, May 18 2008

G.f.: x(1+x+x^2+x^3-x^4)/(1-x)^3. a(n) = 3*a(n-1) -3*a(n-2) + a(n-3), n>5. a(n+1)-a(n) = A016777(n), n>3. - R. J. Mathar, Nov 25 2008

EXAMPLE

a(5) = 33 = (1, 4, 6, 4, 1) dot (1, 3, 3, 1, -2) = (1 + 12 + 18 + 4 - 2).

MAPLE

1, 4, seq((1/2)*(n+1)*(3*n-4), n=3..40); # Emeric Deutsch, May 18 2008

MATHEMATICA

s=-2; lst={1, 4}; Do[s+=n+1; If[n>3, AppendTo[lst, s]], {n, 0, 6!, 3}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2008 *)

PROG

(Magma) [1, 4] cat [(n+1)*(3*n-4)/2: n in [3..50]]; // Vincenzo Librandi, Oct 27 2014

CROSSREFS

Cf. A049777

Sequence in context: A008039 A024986 A028358 * A100440 A027373 A008142

Adjacent sequences:  A140226 A140227 A140228 * A140230 A140231 A140232

KEYWORD

nonn

AUTHOR

Gary W. Adamson, May 13 2008

EXTENSIONS

More terms from Emeric Deutsch, May 18 2008

More terms from Vladimir Joseph Stephan Orlovsky, Oct 25 2008

STATUS

approved

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Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.