Netted matrices
2003 ◽
Vol 2003
(39)
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pp. 2507-2518
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We prove that powers of4-netted matrices (the entries satisfy a four-term recurrenceδai,j=αai−1,j+βai−1,j+γai,j−1) preserve the property of nettedness: the entries of theeth power satisfyδeai,j(e)=αeai−1,j(e)+βeai−1,j−1(e)+γeai,j−1(e), where the coefficients are all instances of the same sequencexe+1=(β+δ)xe−(βδ+αγ)xe−1. Also, we find a matrixQn(a,b)and a vectorvsuch thatQn(a,b)e⋅vacts as a shifting on the general second-order recurrence sequence with parametersa,b. The shifting action ofQn(a,b)generalizes the known property(0111)e⋅(1,0)t=(Fe−1,Fe)t. Finally, we prove some results about congruences satisfied by the matrixQn(a,b).
1992 ◽
Vol 35
(1)
◽
pp. 61-69
◽
2007 ◽
Vol 2007
◽
pp. 1-16
◽
1966 ◽
Vol 295
(1443)
◽
pp. 476-489
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