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A178159 Modified variant of A006645, the self-convolution of the Pell series. 1
1, 2, 8, 22, 68, 188, 532, 1444, 3921, 10446, 27704, 72714, 189912, 492760, 1273064, 3273896, 8389489, 21423994, 54550728, 138520286, 350899964, 886925652, 2237284668, 5633150988, 14159465505, 35535456518, 89053087224, 222870328210, 557074041840, 1390807477040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Analogous series using the Fibonacci numbers as a generator = A089098.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,0,-12,4,4,4,4,1).

FORMULA

(1/2) * [ (1, 4, 14, 44, 131,...) + (1, 0, 2, 0, 5,...)]; where (1, 4, 14, 44,...) = A006645, the self-convolution of the Pell series, and (1, 0, 2, 0, 5,...) = the aerated Pell series.

G.f.: -x*(2*x^3-2*x+1) / ((x^2+2*x-1)^2*(x^4+2*x^2-1)). - Colin Barker, Jul 21 2015

EXAMPLE

(1/2) * (1, 4, 14, 44, 131,...) + (1, 0, 2, 0, 5,...) = (1/2) * (2, 4, 16, 44, 136, 376,...) = (1, 2, 8, 22, 68, 188,...).

MAPLE

A178159 := proc(n)

    if type (n, 'even') then

        (A006645(n+2) + A000129(n/2+1))/2 ;

    else

        A006645(n+2)/2 ;

    fi;

end proc: # R. J. Mathar, Jul 21 2015

PROG

(PARI) Vec(-x*(2*x^3-2*x+1)/((x^2+2*x-1)^2*(x^4+2*x^2-1)) + O(x^40)) \\ Colin Barker, Jul 21 2015

CROSSREFS

Cf. A089098, A006645.

Sequence in context: A102880 A137104 A265951 * A262720 A321573 A137103

Adjacent sequences:  A178156 A178157 A178158 * A178160 A178161 A178162

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Dec 18 2010

EXTENSIONS

Corrected by R. J. Mathar, Jul 21 2015

STATUS

approved

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Last modified October 1 04:31 EDT 2022. Contains 357134 sequences. (Running on oeis4.)