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 A026814 Number of partitions of n in which the greatest part is 8. 23
 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 52, 70, 89, 116, 146, 186, 230, 288, 352, 434, 525, 638, 764, 919, 1090, 1297, 1527, 1801, 2104, 2462, 2857, 3319, 3828, 4417, 5066, 5812, 6630, 7564, 8588, 9749, 11018, 12450, 14012, 15765, 17674 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 1..1000 from Vincenzo Librandi) FORMULA G.f.: x^8 / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^8)). [Colin Barker, Feb 22 2013] a(n) = A008284(n,8). - Robert A. Russell, May 13 2018 a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} 1. - Wesley Ivan Hurt, Jul 04 2019 MATHEMATICA Table[ Length[ Select[ Partitions[n], First[ # ] == 8 & ]], {n, 1, 60} ] CoefficientList[Series[x^8/((1 - x) (1 - x^2) (1 - x^3) (1 - x^4) (1 - x^5) (1 - x^6) (1 - x^7) (1 - x^8)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *) Drop[LinearRecurrence[{1, 1, 0, 0, -1, 0, -1, 0, -1, 0, 1, 2, 1, 0, 1, -1,   -1, -2, -1, -1, 1, 0, 1, 2, 1, 0, -1, 0, -1, 0, -1, 0, 0, 1, 1, -1}, Append[Table[0, {35}], 1], 128], 27] (* Robert A. Russell, May 17 2018 *) PROG (PARI) x='x+O('x^99); concat(vector(8), Vec(x^8/prod(k=1, 8, 1-x^k))) \\ Altug Alkan, May 17 2018 (GAP) List([0..70], n->NrPartitions(n, 8)); # Muniru A Asiru, May 17 2018 CROSSREFS Cf. A026810, A026811, A026812, A026813, A026815, A026816. Sequence in context: A330640 A319474 A218508 * A008637 A008631 A238866 Adjacent sequences:  A026811 A026812 A026813 * A026815 A026816 A026817 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Robert G. Wilson v, Jan 11 2002 a(0)=0 prepended by Seiichi Manyama, Jun 08 2017 STATUS approved

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Last modified February 24 08:17 EST 2020. Contains 332201 sequences. (Running on oeis4.)