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A145302
a(n) = ((7 + sqrt(7))^n + (7 - sqrt(7))^n)/2.
7
1, 7, 56, 490, 4508, 42532, 406112, 3899224, 37532432, 361686640, 3487250816, 33630672544, 324364881344, 3128620091968, 30177356271104, 291080943932800, 2807684251672832, 27082179878242048, 261227779725129728
OFFSET
0,2
COMMENTS
Binomial transform is A152265, inverse binomial transform is A146966.
FORMULA
From R. J. Mathar, Oct 10 2008: (Start)
a(n) = 14*a(n-1) - 42*a(n-2).
G.f.: (1-7x)/(1-14x+42x^2). (End)
a(n) = Sum_{k=0..n} 7^k*A098158(n,k). - Philippe Deléham, Oct 14 2008
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((7+r7)^n+(7-r7)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Oct 20 2008, Jul 09 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008
EXTENSIONS
More terms from R. J. Mathar, Oct 10 2008
Edited by Klaus Brockhaus, Jul 09 2009
STATUS
approved