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A159612
INVERT transform of (1, 3, 1, 3, 1, ...).
16
1, 4, 8, 24, 56, 152, 376, 984, 2488, 6424, 16376, 42072, 107576, 275864, 706168, 1809624, 4634296, 11872792, 30409976, 77901144, 199541048, 511145624, 1309309816, 3353892312, 8591131576, 22006700824, 56371227128, 144398030424, 369882938936, 947475060632, 2427006816376
OFFSET
1,2
COMMENTS
The sequence 1,1,4,8,24,... is an eigensequence of the sequence triangle of 1,3,1,3,1,3,1,..., which is the Riordan array ((1+3x)/(1-x^2),x). - Paul Barry, Feb 10 2011
LINKS
Silvana Ramaj, New Results on Cyclic Compositions and Multicompositions, Master's Thesis, Georgia Southern Univ., 2021. See p. 33.
FORMULA
G.f.: x*(1+3*x)/(1-x-4*x^2). - Philippe Deléham, Mar 01 2012
a(n) = a(n-1) + 4*a(n-2), a(1)=1, a(2)=4. - Vincenzo Librandi, Mar 11 2011
a(n+1) = Sum_{k=0..n} A119473(n,k)*3^k. - Philippe Deléham, Oct 05 2012
a(n) = 2^(-3-n)*((1-sqrt(17))^n*(-5+3*sqrt(17)) + (1+sqrt(17))^n*(5+3*sqrt(17))) / sqrt(17) for n > 0. - Colin Barker, Dec 22 2016
EXAMPLE
a(4) = 24 = (1, 3, 1, 3) dot (8, 4, 1, 1) = (8 + 12, + 1 + 3).
MATHEMATICA
LinearRecurrence[{1, 4}, {1, 4}, 50] (* Vladimir Joseph Stephan Orlovsky, Jul 17 2011 *)
PROG
(PARI) Vec(x*(1+3*x)/(1-x-4*x^2) + O(x^40)) \\ Colin Barker, Dec 22 2016
CROSSREFS
Cf. A119473.
Sequence in context: A153334 A332871 A116719 * A099176 A190156 A291024
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Apr 17 2009
STATUS
approved