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A141533 The first subdiagonal of the array of A141425 and its higher order differences. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 22 22:05 EDT 2017. Contains 283901 sequences.