|
|
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
|
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
|
|
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
|
|
|
FORMULA
|
G.f.: ( -1+3*x-4*x^2 ) / ( (x-1)*(3*x-1)*(2*x-1) ). - Simon Plouffe in his 1992 dissertation.
|
|
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).
|
|
MAPLE
|
|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|