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A087503 a(n) = 3(a(n-2) + 1), with a(0) = 1, a(1) = 3. 8
1, 3, 6, 12, 21, 39, 66, 120, 201, 363, 606, 1092, 1821, 3279, 5466, 9840, 16401, 29523, 49206, 88572, 147621, 265719, 442866, 797160, 1328601, 2391483, 3985806, 7174452, 11957421, 21523359, 35872266, 64570080, 107616801, 193710243 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = a(n-1) + A038754(n).

Partial sums of A038754.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

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

FORMULA

From Hieronymus Fischer, Sep 19 2007, formulas adjusted to offset, Dec 29 2012: (Start)

G.f.: g(x) = (1+2x)/((1-3x^2)(1-x)).

a(n) = (3/2)*(3^((n+1)/2)-1) if n is odd, else a(n) = (3/2)*(5*3^((n-2)/2)-1).

a(n) = (3/2)*(3^floor((n+1)/2) + 3^floor(n/2) - 3^floor((n-1)/2)-1).

a(n) = 3^floor((n+1)/2) + 3^floor((n+2)/2)/2 - 3/2.

a(n) = A132667(a(n+1)) - 1.

a(n) = A132667(a(n-1) + 1) for n > 0.

A132667(a(n)) = a(n-1) + 1 for n > 0.

Also numbers such that: a(0)=1, a(n) = a(n-1) + (p-1)*p^((n+1)/2 - 1) if n is odd, else a(n) = a(n-1) + p^(n/2), where p=3.

(End)

MAPLE

a[0]:=1:a[1]:=3:for n from 2 to 100 do a[n]:=3*a[n-2]+3 od: seq(a[n], n=0..33); # Zerinvary Lajos, Mar 17 2008

MATHEMATICA

RecurrenceTable[{a[0]==1, a[1]==3, a[n]==3(a[n-2]+1)}, a, {n, 40}] (* or *) LinearRecurrence[{1, 3, -3}, {1, 3, 6}, 40] (* Harvey P. Dale, Jan 01 2015 *)

PROG

(MAGMA) [(3/2)*(3^Floor((n+1)/2)+3^Floor(n/2)-3^Floor((n-1)/2)-1): n in [0..40]]; // Vincenzo Librandi, Aug 16 2011

CROSSREFS

Sequences with similar recurrence rules: A027383 (p=2), A133628 (p=4), A133629 (p=5).

Other related sequences for different p: A016116 (p=2), A038754 (p=3), A084221 (p=4), A133632 (p=5).

See A133629 for general formulas with respect to the recurrence rule parameter p.

Related sequences: A132666, A132667, A132668, A132669.

Sequence in context: A215005 A006330 A293636 * A092176 A000991 A095093

Adjacent sequences:  A087500 A087501 A087502 * A087504 A087505 A087506

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 11 2003

EXTENSIONS

Additional comments from Hieronymus Fischer, Sep 19 2007

Edited by N. J. A. Sloane, May 04 2010. I merged two essentially identical entries with different offsets, so some of the formulas may need to be adjusted.

Formulas and MAGMA prog adjusted to offset 0 by Hieronymus Fischer, Dec 29 2012

STATUS

approved

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)