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Search: id:A123569
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| A123569 |
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Number of ways to write n as an ordered sum of 1s, 2s, 3s and 4s such that no 2 precedes any 1 and no 3 precedes any 1 or 2. |
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+0
1
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| 1, 2, 3, 5, 7, 12, 17, 26, 37, 57, 80, 119, 168, 247, 346, 503, 705, 1014, 1417, 2026, 2827, 4015, 5595, 7912, 11009, 15505, 21554, 30260, 42020, 58837, 81639, 114054, 158137, 220521, 305563, 425432, 589179, 819234, 1134015, 1575053, 2179376
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This sequence, along with A124062, are the first two of a sequence of sequences which interpolate between the Fibonacci numbers, A000045 and the partition numbers, A000041.
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FORMULA
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G.f.: A(x) = (1 - x^4)^2 / ((1 - x - x^4)(1 - x^2 - x^4)(1 - x^3 - x^4)) a(n+12) = a(n+11) + a(n+10) + 2a(n+8) - 3a(n+7) - a(n+6) - a(n+5) - 2a(n+4) + 2a(n+3) + a(n+2) + a(n+1) + a(n)
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EXAMPLE
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a(5) = 7 because we can write 5 = 1+1+1+1+1 = 1+1+1+2 = 1+1+3 = 1+2+2 = 1+4 = 2+3 = 4+1.
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MATHEMATICA
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CoefficientList[Normal[Series[ -((x^4 + x^3 - 1)(x^4 + x^2 - 1)(x^4 + x - 1))^(-1) (1 - 2x^4 + x^8), {x, 0, 40}]], x]
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CROSSREFS
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Cf. A124062.
Sequence in context: A024790 A027959 A060730 this_sequence A048816 A080528 A002965
Adjacent sequences: A123566 A123567 A123568 this_sequence A123570 A123571 A123572
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KEYWORD
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easy,nonn
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AUTHOR
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Joel Lewis (jblewis(AT)fas.harvard.edu), Nov 12 2006
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