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 A026811 Number of partitions of n in which the greatest part is 5. 22
 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70, 84, 101, 119, 141, 164, 192, 221, 255, 291, 333, 377, 427, 480, 540, 603, 674, 748, 831, 918, 1014, 1115, 1226, 1342, 1469, 1602, 1747, 1898, 2062, 2233, 2418, 2611, 2818, 3034, 3266, 3507, 3765 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Essentially same as A001401: five zeros followed by A001401. Also number of partitions of n into exactly 5 parts. REFERENCES D. E. Knuth, The Art of Computer Programming, vol. 4, fascicle 3, Generating All Combinations and Partitions, Section 7.2.1.4., p. 56, exercise 31. LINKS Washington Bomfim, Table of n, a(n) for n = 0..10000 FORMULA a(n) = round( ((n^4+10*(n^3+n^2)-75*n -45*n*(-1)^n)) / 2880 ). - Washington Bomfim, Jul 03 2012 G.f.: x^5/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)). - Joerg Arndt, Jul 04 2012 a(n) = A008284(n,5). - Robert A. Russell, May 13 2018 From Gregory L. Simay, Jul 28 2019: (Start) a(2n)   = a(2n-1) + a(n+1) + a(n) - a(n-3) - a(n-4); a(2n+1) = a(2n)   + a(n+3) - a(n-5). (End) MATHEMATICA Table[Count[IntegerPartitions[n], {5, ___}], {n, 0, 55}] (* corrected by Harvey P. Dale, Oct 24 2011 *) Table[Length[IntegerPartitions[n, {5}]], {n, 0, 55}] (* Eric Rowland, Mar 02 2017 *) CoefficientList[Series[x^5/Product[1 - x^k, {k, 1, 5}], {x, 0, 65}], x] (* Robert A. Russell, May 13 2018 *) Drop[LinearRecurrence[{1, 1, 0, 0, -1, -1, -1, 1, 1, 1, 0, 0, -1, -1, 1}, Append[Table[0, {14}], 1], 110], 9] (* Robert A. Russell, May 17 2018 *) PROG (PARI) a(n)=round((n^4+10*(n^3+n^2)-75*n-45*(-1)^n*n)/2880); for(n=0, 10000, print(n, " ", a(n))); /* b-file format */ /* Washington Bomfim, Jul 03 2012 */ (PARI) x='x+O('x^99); concat(vector(5), Vec(x^5/prod(k=1, 5, 1-x^k))) \\ Altug Alkan, May 17 2018 (GAP) List([0..70], n->NrPartitions(n, 5)); # Muniru A Asiru, May 17 2018 CROSSREFS Cf. A026810, A026812, A026813, A026814, A026815, A026816, A002622 (partial sums), A008667 (first differences). Sequence in context: A103232 A062684 A033485 * A001401 A008628 A038499 Adjacent sequences:  A026808 A026809 A026810 * A026812 A026813 A026814 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Robert G. Wilson v, Jan 11 2002 a(0)=0 inserted by Joerg Arndt, Jul 04 2012 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)