cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A256225 Number of partitions of 5n into 5 parts.

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%I A256225 #20 Jun 13 2015 00:55:26
%S A256225 0,1,7,30,84,192,377,674,1115,1747,2611,3765,5260,7166,9542,12470,
%T A256225 16019,20282,25337,31289,38225,46262,55496,66055,78045,91606,106852,
%U A256225 123935,142979,164147,187572,213429,241860,273052,307156,344370,384855,428821,476437,527925
%N A256225 Number of partitions of 5n into 5 parts.
%H A256225 Colin Barker, <a href="/A256225/b256225.txt">Table of n, a(n) for n = 0..1000</a>
%H A256225 <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 A256225 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 A256225 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 A256225 Length /@ (Length /@ IntegerPartitions[5 #, {5}] & /@ Range@ 39) (* _Michael De Vlieger_, Mar 20 2015 *)
%o A256225 (PARI)
%o A256225 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 A256225 (PARI)
%o A256225 concat(0, vector(40, n, k=0; forpart(p=5*n, k++, , [5,5]); k)) \\ _Colin Barker_, Mar 21 2015
%Y A256225 Cf. A001401, A077043, A238340, A256226, A256235.
%K A256225 nonn,easy
%O A256225 0,3
%A A256225 _Colin Barker_, Mar 19 2015