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A000115 Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).
(Formerly M0279 N0098)
6
1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 16, 18, 20, 22, 24, 26, 29, 31, 34, 36, 39, 42, 45, 48, 51, 54, 58, 61, 65, 68, 72, 76, 80, 84, 88, 92, 97, 101, 106, 110, 115, 120, 125, 130, 135, 140, 146, 151, 157, 162, 168, 174, 180, 186, 192, 198, 205, 211, 218, 224, 231, 238 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Number of partitions of n into parts 1, 2, or 5.
First differences are in A008616. First differences of A001304. Pairwise sums of A008720.
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 120, D(n;1,2,5).
M. Jeger, Ein partitions problem ..., Elemente de Math., 13 (1958), 97-120.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 152.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
FORMULA
a(n) = round((n+4)^2/20).
a(n) = a(-8 - n) for all n in Z. - Michael Somos, May 28 2014
EXAMPLE
G.f. = 1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 5*x^6 + 6*x^7 + 7*x^8 + ...
MAPLE
1/((1-x)*(1-x^2)*(1-x^5)): seq(coeff(series(%, x, n+1), x, n), n=0..65);
# next Maple program:
s:=proc(n) if n mod 5 = 0 then RETURN(1); fi; if n mod 5 = 1 then RETURN(0); fi; if n mod 5 = 2 then RETURN(1); fi; if n mod 5 = 3 then RETURN(-1); fi; if n mod 5 = 4 then RETURN(-1); fi; end: f:=n->(2*n^2+16*n+27+5*(-1)^n+8*s(n))/40: seq(f(n), n=0..65); # from Jeger's paper
MATHEMATICA
nn=50; CoefficientList[Series[1/(1-x)/(1-x^2)/(1-x^5), {x, 0, nn}], x] (* Geoffrey Critzer, Jan 20 2013 *)
LinearRecurrence[{1, 1, -1, 0, 1, -1, -1, 1}, {1, 1, 2, 2, 3, 4, 5, 6}, 70] (* Harvey P. Dale, Sep 27 2019 *)
PROG
(Magma) [Round((n+4)^2/20): n in [0..70]]; // Vincenzo Librandi, Jun 23 2011
(PARI) a(n)=(n^2+8*n+26)\20 \\ Charles R Greathouse IV, Jun 23 2011
CROSSREFS
Sequence in context: A017885 A274165 A011874 * A367253 A033552 A062420
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)