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!)
 A256320 Number of partitions of 4n into exactly 3 parts. 4
 0, 1, 5, 12, 21, 33, 48, 65, 85, 108, 133, 161, 192, 225, 261, 300, 341, 385, 432, 481, 533, 588, 645, 705, 768, 833, 901, 972, 1045, 1121, 1200, 1281, 1365, 1452, 1541, 1633, 1728, 1825, 1925, 2028, 2133, 2241, 2352, 2465, 2581, 2700, 2821, 2945, 3072, 3201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1). FORMULA a(n) = A184637(n) for n > 2. a(n) = 2*a(n-1)-a(n-2)+a(n-3)-2*a(n-4)+a(n-5) for n>4. G.f.: -x*(x+1)^3 / ((x-1)^3*(x^2+x+1)). a(n) = 2*(6*n^2+cos((2*Pi*n)/3)-1)/9. - Colin Barker, Jun 06 2016 EXAMPLE For n=2 the 5 partitions of 4*2 = 8 are [1,1,6], [1,2,5], [1,3,4], [2,2,4] and [2,3,3]. MATHEMATICA Length /@ (Total /@ IntegerPartitions[4 #, {3}] & /@ Range[0, 49]) (* Michael De Vlieger, Mar 24 2015 *) CoefficientList[Series[-x (x + 1)^3/((x - 1)^3 (x^2 + x + 1)), {x, 0, 49}], x] (* or *) Table[2 (6 n^2 + Cos[(2 Pi n)/3] - 1)/9, {n, 0, 49}] (* Michael De Vlieger, Jun 06 2016 *) PROG (PARI) concat(0, vector(40, n, k=0; forpart(p=4*n, k++, , [3, 3]); k)) (PARI) concat(0, Vec(-x*(x+1)^3/((x-1)^3*(x^2+x+1)) + O(x^100))) CROSSREFS Cf. A033428 (6n), A256321 (5n), A256322 (7n). Cf. A184637. Sequence in context: A028347 A346379 A354399 * A301693 A038794 A225284 Adjacent sequences: A256317 A256318 A256319 * A256321 A256322 A256323 KEYWORD nonn,easy AUTHOR Colin Barker, Mar 24 2015 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 June 16 13:05 EDT 2024. Contains 373429 sequences. (Running on oeis4.)