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A124502
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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).
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4
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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; internal format)
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OFFSET
| 1,3
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COMMENTS
| If we split this sequence into 5 seperate 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.
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FORMULA
| O.g.f.: x/((1-x)*(x^4+x^3+x^2+x+1)*(1-x-x^2)) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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) [From Gary Detlefs (gedtlefs(AT)aol.com), Dec 10 2010]
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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.
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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 (njas(AT)research.att.com), May 25 2008
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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 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 16 2010]
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CROSSREFS
| Cf. A052952, A004695, A080239, A131132.
Sequence in context: A076027 A056686 A079962 * A173714 A026746 A004699
Adjacent sequences: A124499 A124500 A124501 * A124503 A124504 A124505
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 25 2008
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EXTENSIONS
| Typo in Maple code corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 30 2008
More specific name from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 09 2009
Indices in definition corrected Nov 25 2010 by N. J. A. Sloane
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