The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008795 Molien series for 3-dimensional representation of dihedral group D_6 of order 6. 19
 1, 0, 3, 1, 6, 3, 10, 6, 15, 10, 21, 15, 28, 21, 36, 28, 45, 36, 55, 45, 66, 55, 78, 66, 91, 78, 105, 91, 120, 105, 136, 120, 153, 136, 171, 153, 190, 171, 210, 190, 231, 210, 253, 231, 276, 253, 300, 276, 325, 300, 351, 325, 378, 351, 406, 378, 435, 406, 465, 435, 496, 465, 528, 496 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n-3) is the number of ordered triples of positive integers which are the side lengths of a nondegenerate triangle of perimeter n. - Rob Pratt, Jul 12 2004 a(n) is the number of ways to distribute n identical objects into 3 distinguishable bins so that no bin contains an absolute majority of objects. - Geoffrey Critzer, Mar 17 2010 From Omar E. Pol, Feb 05 2012 (Start:) Also terms of A000217 and A000217-shifted interleaved. Also 0 together with this sequence give the first row of the square array A194801. (End) a(n) is the number of coins left after packing 3-curves coins patterns into fountain of coins base n. Refer to A005169: "A fountain is formed by starting with a row of coins, then stacking additional coins on top so that each new coin touches two in the previous row". See illustration in links. - Kival Ngaokrajang, Oct 12 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Kival Ngaokrajang, Illustration of initial terms Ira Rosenholtz, Problem 1584, Mathematics Magazine, Vol. 72 (1999), p. 408. Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA The signed version with g.f. (1-x^3)/(1-x^2)^3 is the inverse binomial transform of A084861. - Paul Barry, Jun 12 2003 a(n) = binomial(n/2+2, 2) for n even, binomial((n+1)/2, 2) for n odd. - Rob Pratt, Jul 12 2004 From Paul Barry, Jul 29 2004: (Start) a(n-2) interleaves n(n+1)/2 and n(n-1)/2. G.f.: (1-x+x^2)/((1+x)^2*(1-x)^3)). a(n) = (2*n^2 + 6*n + 7 + 3*(2*n+3)*(-1)^n)/16. (End) a(n) = n*(n+1)/2, n = +- 1, +- 2... - Omar E. Pol, Feb 05 2012 From Michael Somos, Feb 01 2018: (Start) Euler transform of length 6 sequence [0, 3, 1, 0, 0, -1]. G.f.: (1 + x^3) / (1 - x^2)^3. a(n) = a(-3-n) for all in Z. (End) MAPLE a:= n-> binomial(n/2+2-3*irem(n, 2)/2, 2): seq(a(n), n=0..70); # Muniru A Asiru, Feb 01 2018 MATHEMATICA Table[If[EvenQ[n], Binomial[n/2+2, 2], Binomial[(n+1)/2, 2]], {n, 0, 70}] CoefficientList[Series[(1+x^3)/(1-x^2)^3, {x, 0, 70}], x] (* Robert G. Wilson v, Feb 05 2012 *) a[ n_]:= Binomial[ Quotient[n, 2] + 2 - Mod[n, 2], 2]; (* Michael Somos, Feb 01 2018 *) a[ n_]:= With[ {m = If[ n < 0, -3 - n, n]}, SeriesCoefficient[ (1 - x + x^2) / ((1 - x)^3 (1 + x)^2), {x, 0, m}]]; (* Michael Somos, Feb 01 2018 *) LinearRecurrence[{1, 2, -2, -1, 1}, {1, 0, 3, 1, 6}, 70] (* Robert G. Wilson v, Feb 01 2018 *) PROG (MAGMA) [(2*n^2+6*n+7)/16+3*(2*n+3)*(-1)^n/16: n in [0..70] ]; // Vincenzo Librandi, Aug 21 2011 (PARI) a(n)=(2*n^2+6*n+7)/16+3*(2*n+3)*(-1)^n/16 \\ Charles R Greathouse IV, Oct 22 2015 (PARI) {a(n) = binomial(n\2 + 2 - n%2, 2)}; /* Michael Somos, Feb 01 2018 */ (GAP) a := [1, 0, 3, 1, 6];; for n in [6..70] do a[n] := a[n-1] + 2*a[n-2] -2*a[n-3] -a[n-4] +a[n-5]; od; a; # Muniru A Asiru, Feb 01 2018 (Sage) [(2*n^2 +6*n +7 +3*(2*n+3)*(-1)^n)/16 for n in (0..70)] # G. C. Greubel, Sep 11 2019 CROSSREFS Cf. A005044. First differences of A053307. Sequence in context: A158822 A226132 A121443 * A165188 A294778 A132180 Adjacent sequences:  A008792 A008793 A008794 * A008796 A008797 A008798 KEYWORD nonn,easy AUTHOR EXTENSIONS Definition clarified by N. J. A. Sloane, Feb 02 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 14 13:27 EDT 2020. Contains 335729 sequences. (Running on oeis4.)