OFFSET
0,3
COMMENTS
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
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,1,-1,-1,1)
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved