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A256225 Number of partitions of 5n into 5 parts. 5

%I

%S 0,1,7,30,84,192,377,674,1115,1747,2611,3765,5260,7166,9542,12470,

%T 16019,20282,25337,31289,38225,46262,55496,66055,78045,91606,106852,

%U 123935,142979,164147,187572,213429,241860,273052,307156,344370,384855,428821,476437,527925

%N Number of partitions of 5n into 5 parts.

%H Colin Barker, <a href="/A256225/b256225.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,0,-2,2,0,1,0,-2,1).

%F G.f.: -x*(x^8+5*x^7+16*x^6+25*x^5+31*x^4+25*x^3+16*x^2+5*x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^2+x+1)).

%e For n=2, the 7 partitions of 10 are [6,1,1,1,1], [5,2,1,1,1], [4,3,1,1,1], [4,2,2,1,1], [3,3,2,1,1], [3,2,2,2,1] and [2,2,2,2,2].

%t Length /@ (Length /@ IntegerPartitions[5 #, {5}] & /@ Range@ 39) (* _Michael De Vlieger_, Mar 20 2015 *)

%o (PARI)

%o concat(0, Vec(-x* (x^8+5*x^7+16*x^6+25*x^5+31*x^4+25*x^3+16*x^2+5*x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)))

%o (PARI)

%o concat(0, vector(40, n, k=0; forpart(p=5*n, k++, , [5,5]); k)) \\ _Colin Barker_, Mar 21 2015

%Y Cf. A001401, A077043, A238340, A256226, A256235.

%K nonn,easy

%O 0,3

%A _Colin Barker_, Mar 19 2015

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)