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A025769
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Expansion of 1/((1-x)(1-x^3)(1-x^8)).
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1
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1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 61, 63, 65, 68, 70, 72, 75, 77, 80, 83, 85, 88
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OFFSET
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0,4
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COMMENTS
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Mark Underwood observed that the number of partitions into four nonzero squares of the squares of primes is given by A025428(A001248(n)) = a(prime(n)-4), cf. sequence A216374. - M. F. Hasler, Sep 16 2012
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LINKS
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Table of n, a(n) for n=0..59.
Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1, 0, 0, 0, 1, -1, 0, -1, 1).
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FORMULA
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a(n) = floor((x^2+12x+c)/48) with 51 <= c <= 58. - M. F. Hasler, Sep 16 2012
a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=2, a(6)=3, a(7)=3, a(8)=4, a(9)=5, a(10)=5, a(11)=6, a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-8)-a(n-9)- a(n-11)+ a(n-12). - Harvey P. Dale, Nov 29 2012
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MATHEMATICA
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CoefficientList[Series[1/((1-x)(1-x^3)(1-x^8)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 0, 1, -1, 0, 0, 0, 1, -1, 0, -1, 1}, {1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6}, 60] (* Harvey P. Dale, Nov 29 2012 *)
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PROG
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(PARI) A025769(n)=((x+6)^2+16)\48 \\ - M. F. Hasler, Sep 16 2012
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CROSSREFS
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Sequence in context: A107631 A029098 A074286 * A103563 A008625 A029148
Adjacent sequences: A025766 A025767 A025768 * A025770 A025771 A025772
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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