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A060961
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Number of ordered partitions of n into 1's, 3's and 5's.
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4
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1, 1, 2, 3, 5, 8, 12, 19, 30, 47, 74, 116, 182, 286, 449, 705, 1107, 1738, 2729, 4285, 6728, 10564, 16587, 26044, 40893, 64208, 100816, 158296, 248548, 390257, 612761, 962125, 1510678, 2371987, 3724369, 5847808, 9181920, 14416967, 22636762, 35543051
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,500
Index to sequences with linear recurrences with constant coefficients, signature (1,0,1,0,1).
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FORMULA
| a(n)=a(n-1)+a(n-3)+a(n-5)
G.f.: (x+x^3+x^5)/(1-(x+x^3+x^5))
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MATHEMATICA
| CoefficientList[Series[(1 + z^2 + z^4)/(1 - z - z^3 - z^5), {z, 0, 100}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
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PROG
| (PARI) { for (n=1, 500, if (n>5, a=a1 + a3 + a5; a5=a4; a4=a3; a3=a2; a2=a1; a1=a, if (n==1, a=a5=1, if (n==2, a=a4=1, if (n==3, a=a3=2, if (n==4, a=a2=3, a=a1=5))))); write("b060961.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 15 2009]
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CROSSREFS
| Cf. A060945 (1's, 2's and 4's).
Sequence in context: A099823 A023436 A024567 * A179018 A205476 A170805
Adjacent sequences: A060958 A060959 A060960 * A060962 A060963 A060964
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KEYWORD
| nonn,easy
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AUTHOR
| Len Smiley (smiley(AT)math.uaa.alaska.edu), May 08 2001
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