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A113254
Corresponds to m = 8 in a family of 4th-order linear recurrence sequences given by a(m,n) = m^4*a(n-4) + (2*m)^2*a(n-3) - 4*a(m-1), a(m,0) = -1, a(m,1) = 4, a(m,2) = -13 + 6*(m-1) + 3*(m-1)^2, a(m,3) = (-8+m^2)^2.
8
-1, 4, 176, 3136, -15616, 123904, 1028096, 4734976, -51183616, 975437824, 1521483776, 205520896, 39241908224, 4227925540864, -10627091267584, 53396107165696, 1029499365883904, 10479050187341824, -71775363146973184, 769363745204862976
OFFSET
0,2
COMMENTS
Conjecture: a(m, 2*n+1) is a perfect square for all m,n (see A113249).
FORMULA
G.f.: (-1+192*x^2+4096*x^3) / ((8*x+1)*(1-8*x)*(64*x^2+4*x+1)).
a(n) = -4*a(n-1) + 256*a(n-3) + 4096*a(n-4) for n > 3. - Colin Barker, May 20 2019
MATHEMATICA
LinearRecurrence[{-4, 0, 256, 4096}, {-1, 4, 176, 3136}, 25] (* Paolo Xausa, Jun 10 2024 *)
PROG
(PARI) Vec(-(1 - 192*x^2 - 4096*x^3) / ((1 - 8*x)*(1 + 8*x)*(1 + 4*x + 64*x^2)) + O(x^25)) \\ Colin Barker, May 20 2019
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Nov 18 2005
STATUS
approved