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A060945
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Number of ordered partitions of n into 1's, 2's and 4's.
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8
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1, 2, 3, 6, 10, 18, 31, 55, 96, 169, 296, 520, 912, 1601, 2809, 4930, 8651, 15182, 26642, 46754, 82047, 143983, 252672, 443409, 778128, 1365520, 2396320, 4205249, 7379697, 12950466, 22726483, 39882198, 69988378, 122821042, 215535903
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 28 2010: (Start)
Prefaced with a 1 = the INVERT transform of the aerated Fibonacci sequence:
(1, 0, 1, 0, 2, 0, 3, 0, 5,...).
a(n) = term (4,4) in the n-th power of the matrix [0,1,0,0; 0,0,1,0; 0,0,0,1; 1,0,1,1]. (End)
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,500
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FORMULA
| a(n) = a(n-1)+a(n-2)+a(n-4). G.f.: (x+x^2+x^4)/(1-x-x^2-x^4)
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MATHEMATICA
| a=b=c=0; d=1; lst={}; Do[AppendTo[lst, e=a+c+d]; a=b; b=c; c=d; d=e, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 28 2010]
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PROG
| (PARI) { for (n=1, 500, if (n>4, a=a1 + a2 + a4; a4=a3; a3=a2; a2=a1; a1=a, if (n==1, a=a4=1, if (n==2, a=a3=2, if (n==3, a=a2=3, a=a1=6)))); write("b060945.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 15 2009]
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CROSSREFS
| Cf. A000045 (1's and 2's only), A023359 (all powers of 2)
Apart from n=0 term, same as unsigned version of A077930.
Sequence in context: A172516 A102702 * A181532 A077930 A023359 A082482
Adjacent sequences: A060942 A060943 A060944 * A060946 A060947 A060948
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KEYWORD
| nonn
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AUTHOR
| Len Smiley (smiley(AT)math.uaa.alaska.edu), May 07 2001
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EXTENSIONS
| More terms from Vladimir Orlovsky (4vladimir(AT)gmail.com), May 28 2010
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