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Search: id:A052539
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| 2, 5, 17, 65, 257, 1025, 4097, 16385, 65537, 262145, 1048577, 4194305, 16777217, 67108865, 268435457, 1073741825, 4294967297, 17179869185, 68719476737, 274877906945, 1099511627777, 4398046511105, 17592186044417
(list; graph; listen)
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OFFSET
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0,1
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 470
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FORMULA
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a(n) = 4^n+1.
a(n) = 4a(n-1) - 3 = 5a(n-1) - 4a(n-2).
G.f.: (2-5*x)/((1-4*x)*(1-x)).
E.g.f.: e^x+e^(4*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 02 2009]
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MAPLE
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spec := [S, {S=Union(Sequence(Union(Z, Z, Z, Z)), Sequence(Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
with(combinat, fibonacci):seq(fibonacci(3, 2^i), i=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
with(finance):seq(mul(cashflows([0, 0, 4], 0 ), k=1..n)+1, n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 02 2008
g:=1/(1-4*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+1, n=0..31); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]
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MATHEMATICA
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Table[4^n + 1, {n, 0, 25}]
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PROGRAM
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sage: [lucas_number2(n, 5, 4) for n in xrange(0, 25)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
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CROSSREFS
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Cf. A000051, A034472, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600 - A074624.
Sequence in context: A150012 A150013 A123166 this_sequence A008932 A062881 A122206
Adjacent sequences: A052536 A052537 A052538 this_sequence A052540 A052541 A052542
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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