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A002783 2*(3^n - 2^n) + 1.
(Formerly M2892 N1159)
7
1, 3, 11, 39, 131, 423, 1331, 4119, 12611, 38343, 116051, 350199, 1054691, 3172263, 9533171, 28632279, 85962371, 258018183, 774316691, 2323474359, 6971471651, 20916512103, 62753730611, 188269580439, 564825518531, 1694510110023, 5083597438931, 15250926534519 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Binomial transform of A095121. - R. J. Mathar, Oct 05 2012
Create a triangle having its left and right border both equal to the n-th row of Pascal's triangle, and internal terms m(i,j)=m(i-1,j-1)+m(i-1,j). Then the sum of all elements equals a(n). - J. M. Bergot, Oct 07 2012, edited by M. F. Hasler, Oct 10 2012
First differences of A090326 (with offset 1). - Wesley Ivan Hurt, Jul 08 2014
REFERENCES
H. Gupta, On a problem in parity, Indian J. Math., 11 (1969), 157-163.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
H. Gupta, On a problem in parity, Indian J. Math., 11 (1969), 157-163. [Annotated scanned copy]
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
FORMULA
G.f.: ( -1+3*x-4*x^2 ) / ( (x-1)*(3*x-1)*(2*x-1) ). - Simon Plouffe in his 1992 dissertation.
a(n+1) - a(n) = 2*A027649(n). - R. J. Mathar, Oct 05 2012
EXAMPLE
For n=3, one has the triangle with left and right border (1,3,3,1):
1
3 3
3 6 3
1 9 9 1, and sum of all elements equal to 39 = a(3).
- J. M. Bergot and M. F. Hasler, Oct 10 2012
MAPLE
A002783:=n->2*(3^n - 2^n)+1: seq(A002783(n), n=0..30); # Wesley Ivan Hurt, Jul 08 2014
MATHEMATICA
CoefficientList[Series[(-1 + 3*x - 4*x^2)/((x - 1)*(3*x - 1)*(2*x - 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 08 2014 *)
PROG
(Magma) [2*(3^n - 2^n)+1 : n in [0..30]]; // Wesley Ivan Hurt, Jul 08 2014
(PARI) a(n)=2*(3^n-2^n)+1 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Sequence in context: A089579 A227638 A166336 * A289834 A007482 A134760
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Wesley Ivan Hurt, Jul 08 2014
STATUS
approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)