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A213763
Principal diagonal of the convolution array A213762.
3
1, 11, 43, 127, 331, 807, 1891, 4319, 9691, 21463, 47059, 102351, 221131, 475079, 1015747, 2162623, 4587451, 9699255, 20447155, 42991535, 90177451, 188743591, 394264483, 822083487, 1711275931, 3556769687, 7381974931
OFFSET
1,2
COMMENTS
Create a triangle with first column T(n,1)=1+4*n for n=0,1,2... The remaining terms T(r,c)=T(r,c-1)+T(r-1,c-1). The sum of the terms in row(n)=a(n+1). - J. M. Bergot, Dec 18 2012
FORMULA
a(n) = -1 + 2^n - 4*n + n*2^(n+1).
a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).
G.f.: x*(1 + 5*x - 10*x^2)/(1 - 3*x + 2*x^2 )^2.
MATHEMATICA
(See A213762.)
LinearRecurrence[{6, -13, 12, -4}, {1, 11, 43, 127}, 30] (* Harvey P. Dale, Apr 13 2017 *)
CROSSREFS
Sequence in context: A142039 A196153 A373060 * A302226 A201714 A269422
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 20 2012
STATUS
approved