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A124502 a(1)=a(2)=1; thereafter, a(n+1) = a(n) + a(n-1) + 1 if n is a multiple of 5, otherwise a(n+1) = a(n) + a(n-1). 4
1, 1, 2, 3, 5, 9, 14, 23, 37, 60, 98, 158, 256, 414, 670, 1085, 1755, 2840, 4595, 7435, 12031, 19466, 31497, 50963, 82460, 133424, 215884, 349308, 565192, 914500, 1479693, 2394193, 3873886, 6268079, 10141965, 16410045, 26552010, 42962055, 69514065, 112476120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If we split this sequence into 5 separate sequences of n mod 5, each individual sequence is of the form a(n) = 12*a(n-1) - 10*a(n-2) - a(n-3). For example, 12*98 - 10*9 - 1 = 1085. This is the same recurrence exhibited in A138134 and the n mod 5 =0 sequence...5, 60, 670, 7435 is A138134.

LINKS

Table of n, a(n) for n=1..40.

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

FORMULA

O.g.f.: x/((1-x)*(x^4 + x^3 + x^2 + x + 1)*(1 - x - x^2)). - R. J. Mathar, May 30 2008

a(n+5) = a(n) + Fibonacci(n+5), n>5.

a(n) = 12*a(n-5) - 10*a(n-10) - a(n-15). - Gary Detlefs, Dec 10 2010

EXAMPLE

a(6) = a(5) + a(4) + 1 = 5 + 3 + 1 = 9 because n=5 is a multiple of 5.

a(7) = a(6) + a(5) = 9 + 5 = 14 because n=6 is not a multiple of 5.

MAPLE

A124502:=proc(n) option remember; local t1; if n <= 2 then return 1; fi: if n mod 5 = 1 then t1:=1 else t1:=0; fi: procname(n-1)+procname(n-2)+t1; end proc; [seq(A124502(n), n=1..100)]; # N. J. A. Sloane, May 25 2008

MATHEMATICA

a=0; b=0; lst={a, b}; Do[z=a+b+1; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z, {n, 4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 16 2010 *)

nxt[{n_, a_, b_}]:={n+1, b, If[Divisible[n, 5], a+b+1, a+b]}; NestList[nxt, {2, 1, 1}, 40][[All, 2]] (* or *) LinearRecurrence[{1, 1, 0, 0, 1, -1, -1}, {1, 1, 2, 3, 5, 9, 14}, 40] (* Harvey P. Dale, Jun 15 2017 *)

CROSSREFS

Cf. A052952, A004695, A080239, A131132.

Sequence in context: A079962 A244986 A293547 * A251572 A173714 A026746

Adjacent sequences:  A124499 A124500 A124501 * A124503 A124504 A124505

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 25 2008

EXTENSIONS

Typo in Maple code corrected by R. J. Mathar, May 30 2008

More specific name from R. J. Mathar, Dec 09 2009

Indices in definition corrected by N. J. A. Sloane, Nov 25 2010

STATUS

approved

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Last modified June 25 10:10 EDT 2019. Contains 324351 sequences. (Running on oeis4.)