OFFSET
0,2
COMMENTS
First bisection of A005919. - Bruno Berselli, Feb 07 2012
a(n) = the second level of difference between the sum of the terms in the n+1 X n+1 matrices and those in the n X n matrices starting at n=1 for an array constructed by using the terms in A016813 as the antidiagonals; the first few antidiagonals are 1; 5,9; 13,17,21; 25,29,33,37. - J. M. Bergot, Jul 05 2013
[More formally: (sum[m(n+1),j {j=0..n+1}]+sum[m(i,n+1) {i=0..n}]) - (sum[m(n,j) {j=0...n}] + sum[m(i,n) {i=0..n-1}])=a(n)]
[The first five rows begin: 1,9,21,37,57; 5,17,33,53,77; 13,29,49,73,101;25,45,69,97,129; 41,65,93,125,161]
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (1+x)*(1+26*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 07 2012
E.g.f.: (x*(x+1)*28+2)*e^x-1. - Gopinath A. R., Feb 14 2012
Sum_{n>=0} 1/a(n) = 3/4 + sqrt(14)/56*Pi*coth(Pi/sqrt 14) = 1.05615979263340... - R. J. Mathar, May 07 2024
a(n) = 2*A158482(n), n>0. - R. J. Mathar, May 07 2024
MATHEMATICA
Join[{1}, 28 Range[40]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)
LinearRecurrence[{3, -3, 1}, {1, 30, 114, 254}, 40] (* Robert G. Wilson v, Jul 06 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved