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

1, -1, -2, 23, 28, -7, 22, 251, 376, 149, 658, 3143, 5188, 4913, 13102, 42611, 75376, 101549, 232618, 612863, 1137148, 1831433, 3928582, 9185771, 17574376, 31162949, 64717378, 141392183, 275609908, 515347553, 1052218462, 2212053731, 4359537376, 8396224349

Offset

1,3

Links

Table of n, a(n) for n=1..34.

Formula

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

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]

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

Example

A141425 and its first, second, third differences etc. in followup rows define an array T(n,m):
..1...2...4...5...7...8...1...2...4...5...
..1...2...1...2...1..-7...1...2...1...2...
..1..-1...1..-1..-8...8...1..-1...1..-1...
.-2...2..-2..-7..16..-7..-2...2..-2..-7...
..4..-4..-5..23.-23...5...4..-4..-5..23...
.-8..-1..28.-46..28..-1..-8..-1..28.-46...
..7..29.-74..74.-29..-7...7..29.-74..74...
.22.-103.148.-103..22..14..22.-103.148.-103...
-125.251.-251.125..-8...8.-125.251.-251.125...
376.-502.376.-133..16.-133.376.-502.376.-133...
Then a(n) = T(n+1,n) .

Crossrefs

Sequence in context: A086557 A042797 A041649 * A045391 A154758 A156614

Adjacent sequences: A141530 A141531 A141532 * A141534 A141535 A141536

Keyword

sign

Author

Paul Curtz, Aug 12 2008

Extensions

Edited and extended by R. J. Mathar, Nov 22 2009

Status

approved