A141533 - OEIS

%I #4 Mar 30 2012 18:51:59

%S 1,-1,-2,23,28,-7,22,251,376,149,658,3143,5188,4913,13102,42611,75376,

%T 101549,232618,612863,1137148,1831433,3928582,9185771,17574376,

%U 31162949,64717378,141392183,275609908,515347553,1052218462,2212053731,4359537376,8396224349

%N The first subdiagonal of the array of A141425 and its higher order differences.

%F a(2*n)+a(2*n+1)= 0, 21, 21, 273, 525, 3801,... (multiples of 21).

%F a(n)= +a(n-1) -a(n-2) +3*a(n-3) +6*a(n-4). G.f.: x*(1-2*x+21*x^3)/((1-2*x) * (1+x) * (3*x^2+1)). [R. J. Mathar, Nov 22 2009]

%F a(n)= (3*(-1)^n+2^n-A128019(n+1))/2. [R. J. Mathar, Nov 22 2009]

%e A141425 and its first, second, third differences etc. in followup rows define an array T(n,m):

%e ..1...2...4...5...7...8...1...2...4...5...

%e ..1...2...1...2...1..-7...1...2...1...2...

%e ..1..-1...1..-1..-8...8...1..-1...1..-1...

%e .-2...2..-2..-7..16..-7..-2...2..-2..-7...

%e ..4..-4..-5..23.-23...5...4..-4..-5..23...

%e .-8..-1..28.-46..28..-1..-8..-1..28.-46...

%e ..7..29.-74..74.-29..-7...7..29.-74..74...

%e .22.-103.148.-103..22..14..22.-103.148.-103...

%e -125.251.-251.125..-8...8.-125.251.-251.125...

%e 376.-502.376.-133..16.-133.376.-502.376.-133...

%e Then a(n) = T(n+1,n) .

%K sign

%O 1,3

%A _Paul Curtz_, Aug 12 2008

%E Edited and extended by _R. J. Mathar_, Nov 22 2009