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A017821 Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8). 1
1, 0, 0, 1, 1, 1, 2, 3, 4, 5, 8, 12, 16, 23, 34, 48, 68, 98, 141, 201, 287, 412, 590, 843, 1207, 1729, 2474, 3540, 5068, 7255, 10383, 14861, 21273, 30449, 43581, 62380, 89289, 127802, 182927, 261833, 374774 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
COMMENTS
Number of compositions (ordered partitions) of n into parts 3, 4, 5, 6, 7 and 8. - Ilya Gutkovskiy, May 25 2017
LINKS
FORMULA
a(n) = a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) for n>7. - Vincenzo Librandi, Jun 27 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[3, 8]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0, 0, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 1, 1, 1, 2, 3}, 60] (* Harvey P. Dale, Mar 29 2022 *)
PROG
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^3-x^4-x^5-x^6-x^7-x^8)))); /* or */ I:=[1, 0, 0, 1, 1, 1, 2, 3]; [n le 8 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013
CROSSREFS
Sequence in context: A094087 A225132 A240216 * A113439 A274112 A222105
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)