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A141533 The first subdiagonal of the array of A141425 and its higher order differences.

%I A141533 #4 Mar 30 2012 18:51:59
%S A141533 1,-1,-2,23,28,-7,22,251,376,149,658,3143,5188,4913,13102,42611,75376,
%T A141533 101549,232618,612863,1137148,1831433,3928582,9185771,17574376,
%U A141533 31162949,64717378,141392183,275609908,515347553,1052218462,2212053731,4359537376,8396224349
%N A141533 The first subdiagonal of the array of A141425 and its higher order differences.
%F A141533 a(2*n)+a(2*n+1)= 0, 21, 21, 273, 525, 3801,... (multiples of 21).
%F A141533 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 A141533 a(n)= (3*(-1)^n+2^n-A128019(n+1))/2. [R. J. Mathar, Nov 22 2009]
%e A141533 A141425 and its first, second, third differences etc. in followup rows define an array T(n,m):
%e A141533 ..1...2...4...5...7...8...1...2...4...5...
%e A141533 ..1...2...1...2...1..-7...1...2...1...2...
%e A141533 ..1..-1...1..-1..-8...8...1..-1...1..-1...
%e A141533 .-2...2..-2..-7..16..-7..-2...2..-2..-7...
%e A141533 ..4..-4..-5..23.-23...5...4..-4..-5..23...
%e A141533 .-8..-1..28.-46..28..-1..-8..-1..28.-46...
%e A141533 ..7..29.-74..74.-29..-7...7..29.-74..74...
%e A141533 .22.-103.148.-103..22..14..22.-103.148.-103...
%e A141533 -125.251.-251.125..-8...8.-125.251.-251.125...
%e A141533 376.-502.376.-133..16.-133.376.-502.376.-133...
%e A141533 Then a(n) = T(n+1,n) .
%K A141533 sign
%O A141533 1,3
%A A141533 _Paul Curtz_, Aug 12 2008
%E A141533 Edited and extended by _R. J. Mathar_, Nov 22 2009