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A105963 Expansion of (4*x+1)/(1-x-3*x^2). 3
1, 5, 8, 23, 47, 116, 257, 605, 1376, 3191, 7319, 16892, 38849, 89525, 206072, 474647, 1092863, 2516804, 5795393, 13345805, 30731984, 70769399, 162965351, 375273548, 864169601, 1989990245, 4582499048, 10552469783, 24299966927 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Inversion of the periodic sequence with initial period (1,4,-1,-4). Sequence appears to have the property: for m > n, if s divides both a(n) and a(m) then s also divides a(2*m-n). Ex. 23 divides both a(3) = 23 and a(25) = 1989990245; 23 also divides a(2*25-3) = a(47) = 185518234185384428 = (2)^2*(23)*(131)*(15393149202239).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,3).

FORMULA

a(n) = A006130(n)+4*A006130(n-1) = A006130(n+1)+A006130(n-1). - R. J. Mathar, Dec 12 2009

MATHEMATICA

CoefficientList[Series[(4 x + 1) / (1 - x - 3 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 20 2013 *)

PROG

Floretion Algebra Multiplication Program, FAMP Code: 1jesforseq[.5'k + .5k' + 2'kk' + 2e]

(PARI) Vec((4*x+1)/(1-x-3*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

(MAGMA) I:=[ 1, 5]; [n le 2 select I[n] else Self(n-1)+3*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jul 20 2013

CROSSREFS

Cf. A006130, A105476, A274977.

Sequence in context: A092733 A116884 A192651 * A270125 A264797 A270905

Adjacent sequences:  A105960 A105961 A105962 * A105964 A105965 A105966

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Apr 28 2005

STATUS

approved

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Last modified August 20 13:04 EDT 2017. Contains 290835 sequences.