reviewed

approved

proposed

reviewed

editing

proposed

<a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 1, -2, 1, 0, 0, 1, -2, 2, -3, 3, -2, 2, -1, 0, 0, -1, 2, -1, 1, -2, 1).

(PARI) Vec(x^5*(1-x+x^2)*(1-x^3+x^6)/((1-x)^5*(1+x)^2*(1+x^2)*(1+x+x^2)*(1-x+x^2-x^3+x^4)*(1+x^4)*(1+x+x^2+x^3+x^4)) + O(x^70)) \\ Jinyuan Wang, Feb 28 2020

approved

editing

proposed

approved

editing

proposed

(End) [Recurrence Conjectures verified by Wesley Ivan Hurt, Aug 24 2019]

proposed

editing

editing

proposed

<a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 1, -2, 1, 0, 0, 1, -2, 2, -3, 3, -2, 2, -1, 0, 0, -1, 2, -1, 1, -2, 1).

(End) [Recurrence verified by _Wesley Ivan Hurt_, Aug 24 2019]

Table[Sum[Sum[Sum[Sum[Mod[k, 2], {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]

LinearRecurrence[{2, -1, 1, -2, 1, 0, 0, 1, -2, 2, -3, 3, -2, 2, -1,

0, 0, -1, 2, -1, 1, -2, 1}, {0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8,

11, 14, 18, 22, 28, 33, 40, 47, 56, 65}, 50]

Figure 1: The partitions of n into 5 parts for n = 10:, 11, ..

1+1+1+1+610

1+1+1+2+59

1+1+1+3+48

1+1+2+21+4+7

1+1+21+35+36

1+1+1+1+9 1+21+2+2+38

2 1+1+1+2+28 1+1+2+23+7

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1+1+1+3+7 1+1+2+4+6

1+1+1+4+6 1+1+2+5+5

1+1+1+5+5 1+1+3+3+6

1+1+1+1+8 1+1+2+2+7 1+1+3+4+5

1+1+1+2+7 1+1+2+3+6 1+1+4+4+4

1+1+1+3+6 1+1+2+4+5 1+2+2+2+7

1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6

1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5

1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5

1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4

1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4

1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6

1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5

1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4

1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4

2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3

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n | 10 11 12 13 14 ...

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a(n) | 5 7 8 11 14 ...

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