

A084219


Inverse binomial transform of A053088.


2



1, 1, 4, 8, 20, 44, 100, 220, 484, 1052, 2276, 4892, 10468, 22300, 47332, 100124, 211172, 444188, 932068, 1951516, 4077796, 8505116, 17709284, 36816668, 76429540, 158451484, 328087780, 678545180, 1401829604
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OFFSET

0,3


COMMENTS

Unsigned, starting with offset 1: generated from iterates of M * [1,1,1,...]
where M = a tridiagonal matrix with [0,1,1,1,...] as the main diagonal,
[1,1,1,...] as the uperdiagonal and [2,0,0,0,...] as the subdiagonal. (End)
Define a triangle via T(n,0) = T(n,n) = A001045(n) and T(r,c) = T(r1,c1) + T(r1,c). The row sums of the triangle are s(n) = 0, 2, 4, 12, ... = 2*A059570(n), and their first differences are s(n+1)s(n) = 2*a(n). J. M. Bergot, May 15 2013


LINKS



FORMULA

a(n) = (4  3*n*(2)^(n1) + 5*(2)^n)/9.
a(n) = (1/4) + Sum_{k=0..n} (2)^k*(k+3)/4.
G.f.: (1+x)^2/((1x)(1+2x)^2).


MATHEMATICA

LinearRecurrence[{3, 0, 4}, {1, 1, 4}, 30] (* Harvey P. Dale, Dec 16 2016 *)


CROSSREFS



KEYWORD

easy,sign


AUTHOR



STATUS

approved



