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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 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)); (From Jeger's paper:) 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; MATHEMATICA nn=50; CoefficientList[Series[1/(1-x)/(1-x^2)/(1-x^5), {x, 0, nn}], x]  (* Geoffrey Critzer, Jan 20 2013 *) 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 Cf. A001304, A008616, A008720. Sequence in context: A017885 A274165 A011874 * A033552 A062420 A089197 Adjacent sequences:  A000112 A000113 A000114 * A000116 A000117 A000118 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 16 01:15 EST 2019. Contains 319184 sequences. (Running on oeis4.)