The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A050531 Number of multigraphs with loops on 3 nodes with n edges. 10
 1, 2, 6, 14, 28, 52, 93, 152, 242, 370, 546, 784, 1103, 1512, 2040, 2706, 3534, 4554, 5803, 7304, 9108, 11252, 13780, 16744, 20205, 24206, 28826, 34126, 40176, 47056, 54857, 63648, 73542, 84630, 97014, 110808, 126139, 143108, 161868, 182546, 205282 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is also the number of multigraphs (no loops allowed) on 3 nodes with n edges of two colors. - Geoffrey Critzer, Aug 10 2015 LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-3,0,6,0,-3,-2,1,2,-1). FORMULA G.f.: (x^6+x^4+2*x^3+x^2+1)/((x^3-1)^2*(x^2-1)^2*(x-1)^2). a(n) = ceiling((-1)^n*A076118(n+1)/9+(-1)^n*n/32+(4009/4320)*n+(1/2)*n^2+(5/36)*n^3+(1/48)*n^4+(1/720)*n^5). - Robert Israel, Aug 07 2015 a(n) = (A+B+C)/6 where A = binomial(n+5,5); B = (n+2)*(n+3)*(n+4)/8 if n even, B = (n+1)*(n+3)*(n+5)/8 if n odd; C = 2*((n/3) + 1) if n divisible by 3, C = 0 if n not divisible by 3. - David Pasino, Jul 06 2019 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - 3*a(n-4) + 6*a(n-6) - 3*a(n-8) - 2*a(n-9) + a(n-10) + 2*a(n-11) - a(n-12) for n>11. - Colin Barker, Jul 07 2019 MAPLE a076118:= gfun:-rectoproc({a(n+4) = 2*a(n+3)-3*a(n+2)+2*a(n+1)-a(n), a(0)=0, a(1)=1, a(2)=1, a(3)=-1}, a(n), remember): f:= n -> ceil((-1)^n*a076118(n+1)/9+(-1)^n*n/32+(4009/4320)*n+(1/2)*n^2+(5/36)*n^3+(1/48)*n^4+(1/720)*n^5): map(f, [\$0..100]); # Robert Israel, Aug 07 2015 MATHEMATICA < 1/(1 - x^i), {i, 1, n^2 - n}], {x, 0, nn}], x] (* Geoffrey Critzer, Aug 07 2015 *) CoefficientList[Series[(x^6 + x^4 + 2 x^3 + x^2 + 1)/((x^3 - 1)^2 (x^2 - 1)^2 (x - 1)^2), {x, 0, 45}], x] (* Vincenzo Librandi, Aug 08 2015 *) PROG (PARI) Vec((x^6+x^4+2*x^3+x^2+1)/((x^3-1)^2*(x^2-1)^2*(x-1)^2) + O(x^40)) \\ Colin Barker, Jul 07 2019 CROSSREFS Column k=3 of A290428. Cf. A076118, A002620, A290428. Sequence in context: A256058 A294867 A033547 * A290699 A027083 A249665 Adjacent sequences: A050528 A050529 A050530 * A050532 A050533 A050534 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Dec 29 1999 STATUS approved

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

Last modified May 23 17:39 EDT 2024. Contains 372765 sequences. (Running on oeis4.)