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A139482
Binomial transform of [1, 1, 2, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, ...].
3
1, 2, 5, 11, 20, 32, 47, 65, 86, 110, 137, 167, 200, 236, 275, 317, 362, 410, 461, 515, 572, 632, 695, 761, 830, 902, 977, 1055, 1136, 1220, 1307, 1397, 1490, 1586, 1685, 1787, 1892, 2000, 2111, 2225
OFFSET
1,2
COMMENTS
A007318 * [1, 1, 2, 1, -1, 1, -1, 1, ...].
The quadratic expression for a(n) follows at once by taking into account that the alternate row sums in the Pascal triangle are equal to zero (starting with the second row). - Emeric Deutsch, May 03 2008
For n > 1, 3*(8*a(n) - 13) = A016945(n-2)^2. - Vincenzo Librandi, Feb 15 2012
FORMULA
G.f.: (x^3+2*x^2-x+1)/(-x^3+3*x^2-3*x+1). - Alexander R. Povolotsky, Apr 24 2008
a(n) = (10 - 9*n + 3*n^2)/2 for n >= 2. - Emeric Deutsch, May 03 2008
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=2, a(3)=5, a(4)=11. - Harvey P. Dale, May 02 2015
EXAMPLE
a(4) = 11 = (1, 3, 3, 1) dot (1, 1, 2, 1) = (1 + 3 + 6 + 1).
MAPLE
1, seq((10+3*n^2-9*n)*1/2, n=2..40); # Emeric Deutsch, May 03 2008
MATHEMATICA
Join[{1, 2}, FoldList[##+3&, 5, 3*Range@100]] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011 *)
LinearRecurrence[{3, -3, 1}, {1, 2, 5, 11}, 40] (* Harvey P. Dale, May 02 2015 *)
CROSSREFS
Sequence in context: A178316 A179632 A093871 * A038377 A261227 A022908
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Apr 23 2008
EXTENSIONS
More terms from Emeric Deutsch, May 03 2008
STATUS
approved