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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 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 May 7 23:48 EDT 2021. Contains 343652 sequences. (Running on oeis4.)