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A099098 Quadrisection of a Padovan sequence. 6
1, 1, 4, 12, 37, 114, 351, 1081, 3329, 10252, 31572, 97229, 299426, 922111, 2839729, 8745217, 26931732, 82938844, 255418101, 786584466, 2422362079, 7459895657, 22973462017, 70748973084, 217878227876, 670976837021, 2066337330754 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Quadrisection of sequence with g.f. 1/(1-x^2-x^3), or A000931(n+3).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,3,1).

FORMULA

G.f.: (1-x-x^2)/(1-2x-3x^2-x^3); a(n)=sum{k=0..2n, binomial(k, 4n-2k)}; a(n)=2a(n-1)+3a(n-2)+a(n-3); a(n)=A000931(4n+3).

a(n) = Sum [k=0..n, C(2n-k, 2k) ].

EXAMPLE

1 + x + 4*x^2 + 12*x^3 + 37*x^4 + 114*x^5 + 351*x^6 + ...

MATHEMATICA

LinearRecurrence[{2, 3, 1}, {1, 1, 4}, 40] (* Harvey P. Dale, Aug 23 2011 *)

CROSSREFS

Bisection of A005251.

Sequence in context: A101555 A033130 A196918 * A019481 A019480 A192907

Adjacent sequences:  A099095 A099096 A099097 * A099099 A099100 A099101

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 29 2004

STATUS

approved

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Last modified March 19 04:18 EDT 2019. Contains 321311 sequences. (Running on oeis4.)