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A008673 Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)). 2
1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 16, 19, 21, 24, 27, 30, 34, 38, 42, 46, 51, 56, 61, 67, 73, 79, 86, 93, 100, 108, 116, 125, 134, 143, 153, 163, 174, 185, 197, 209, 221, 235, 248, 262, 277, 292, 308, 324, 341, 358, 376, 395, 414, 434, 454, 475, 497, 519, 542, 566, 590 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of partitions of n into parts 1, 3, 5, and 7. - Joerg Arndt, Jul 08 2013

Number of partitions (d1,d2,d3,d4) of n such that 0 <= d1/1 <= d2/2 <= d3/3 <= d4/4. - Seiichi Manyama, Jun 04 2017

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 234

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,1,-1,1,-2,1,-1,1,-1,1,0,1,-1).

FORMULA

a(n) = floor((n^3 + 24*n^2 + 171*n + 630)/630). - Tani Akinari, Jul 08 2013

a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - 2*a(n-8) + a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) + a(n-15) - a(n-16). - David Neil McGrath, Feb 14 2015

EXAMPLE

There are a(7)=5 partitions of n=7 into parts 1, 3, 5, and 7: (7), (511), (331), (31111), and (1111111). - David Neil McGrath, Feb 14 2015

MAPLE

seq(coeff(series(1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)), x, n+1), x, n), n = 0 .. 70); # G. C. Greubel, Sep 08 2019

MATHEMATICA

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^5)(1-x^7)), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 22 2013 *)

LinearRecurrence[{1, 0, 1, -1, 1, -1, 1, -2, 1, -1, 1, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 16, 19}, 70] (* Harvey P. Dale, Jul 08 2019 *)

PROG

(PARI) vector(70, n, m=n-1; (m^3+24*m^2+171*m+630)\630 ) \\ G. C. Greubel, Sep 08 2019

(MAGMA) [Floor((n^3+24*n^2+171*n+630)/630): n in [0..70]]; // G. C. Greubel, Sep 08 2019

(Sage) [floor((n^3+24*n^2+171*n+630)/630) for n in (0..70)] # G. C. Greubel, Sep 08 2019

(GAP) List([0..70], n-> Int((n^3+24*n^2+171*n+630)/630) ); # G. C. Greubel, Sep 08 2019

CROSSREFS

Cf. A259094.

Sequence in context: A065459 A011873 A173151 * A133564 A017863 A242634

Adjacent sequences:  A008670 A008671 A008672 * A008674 A008675 A008676

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)