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A093467 a(1) = 1, a(2) = 2; for n >= 2, a(n+1) = a(n) + Sum_{i = 1..n} (a(i) - a(1)). 3
1, 2, 3, 6, 14, 35, 90, 234, 611, 1598, 4182, 10947, 28658, 75026, 196419, 514230, 1346270, 3524579, 9227466, 24157818, 63245987, 165580142, 433494438, 1134903171, 2971215074, 7778742050, 20365011075, 53316291174, 139583862446 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

K. Kuhapatanakul, On the Sums of Reciprocal Generalized Fibonacci Numbers, J. Int. Seq. 16 (2013) #13.7.1. See Theorem 3 p.3.

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

FORMULA

a(n) = 3*a(n-1) - a(n-2) - 1, n > 3. - Robert G. Wilson v, Apr 08 2004

G.f.: x - x^2*(2*x-1)*(x-2) / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Sep 06 2014

MATHEMATICA

a[1] = 1; a[2] = 2; a[n_] := a[n] = a[n - 1] + Sum[a[i] - a[1], {i, n - 1}]; Table[ a[n], {n, 30}]

Join[{1}, LinearRecurrence[{4, -4, 1}, {2, 3, 6}, 30]] (* Vincenzo Librandi, Feb 08 2017 *)

PROG

(PARI) a(n)=if(n==1, 1, if(n==2, 2, a(n-1)+sum(i=1, n-1, a(i)-a(1)))) \\ Edward Jiang, Sep 06 2014

(ALGOL-60) begin integer procedure A(k, x1, x2, x3);

    value k; integer k;

    integer x1, x2, x3;

    begin integer procedure b;

        begin

            k:= k - 1;

            B:= A := A (k, B, x1, x2);

        end;

        A := if k <= 0 then x2 + x3 else B;

    end;

    integer i;

    for i:= 0 step 1 until 20 do

        print (A (i, 1, 1, 0));

end

comment The above is a simplified Man or Boy Test program (cf. A132343), omitting the negative parameters from the original. - Leonid Broukhis, Feb 07 2017

(MAGMA) I:=[2, 3, 6]; [1] cat [n le 3 select I[n] else  4*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 08 2017

CROSSREFS

Cf. A093468.

Essentially the same as A032908.

Sequence in context: A190166 A238823 A002995 * A246640 A080408 A275774

Adjacent sequences:  A093464 A093465 A093466 * A093468 A093469 A093470

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Apr 07 2004

EXTENSIONS

More terms from Robert G. Wilson v, Apr 08 2004

STATUS

approved

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Last modified May 7 02:20 EDT 2021. Contains 343636 sequences. (Running on oeis4.)