

A102000


a(0),...,a(3) = 1, 2, 4, 8; thereafter a(n) = a(n1) + 2*a(n2) + 4*a(n3) + 8*a(n4), n>3.


2



1, 2, 4, 8, 32, 80, 208, 560, 1552, 4144, 11152, 30128, 81424, 219440, 592016, 1597616, 4310800, 11629616, 31377808, 84661168, 228421648, 616292144, 1662802576, 4486362800, 12104509712, 32658782768, 88115674000, 237742180784
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OFFSET

0,2


COMMENTS

Based on taking the nth power of the matrix M = [1 1 1 1 / 2 0 0 0 / 0 2 0 0 / 0 0 2 0] that generates the D_4 lattice.
a(n)/a(n1) tends to 2.698068913... an eigenvalue of M and a root of the characteristic polynomial x^4  x^3  2*x^2  4*x  8.


LINKS



FORMULA

G.f.: (1x+4*x^3)/(1+x+2*x^2+4*x^3+8*x^4). [R. J. Mathar, Feb 13 2010]


MATHEMATICA

LinearRecurrence[{1, 2, 4, 8}, {1, 2, 4, 8}, 28] (* Hugo Pfoertner, Dec 11 2022 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



