A052367 Number of nonnegative integer 5 X 5 matrices with sum of elements equal to n, under row and column permutations.

1, 1, 4, 10, 33, 91, 277, 792, 2341, 6654, 18802, 51508, 138147, 359457, 910756, 2240915, 5365106, 12495406, 28353714, 62725603, 135469991, 285904968, 590347527, 1193817552, 2366907846, 4605225266, 8801576140, 16538061290

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

G.f.: - (x^86 - 3*x^85 + 9*x^84 + 12*x^83 + 59*x^82 + 116*x^81 + 452*x^80 + 736*x^79 + 2080*x^78 + 3344*x^77 + 7312*x^76 + 11708*x^75 + 21793*x^74 + 32869*x^73 + 55563*x^72 + 79389*x^71 + 123072*x^70 + 168321*x^69 + 243961*x^68 + 319938*x^67 + 438431*x^66 + 553731*x^65 + 724251*x^64 + 885383*x^63 + 1111989*x^62 + 1318149*x^61 + 1600579*x^60 + 1845557*x^59 +

2172889*x^58 + 2444070*x^57 + 2798839*x^56 + 3076865*x^55 + 3436180*x^54 + 3696058*x^53 + 4034590*x^52 + 4250683*x^51 + 4541020*x^50 + 4689359*x^49 + 4909073*x^48 + 4972196*x^47 + 5102026*x^46 + 5069013*x^45 + 5102464*x^44 + 4971700*x^43 + 4909948*x^42 + 4688757*x^41 + 4542211*x^40 + 4249809*x^39 + 4036170*x^38 + 3694857*x^37 + 3438025*x^36 +

3075494*x^35 + 2800760*x^34 + 2442552*x^33 + 2174743*x^32 + 1843864*x^31 + 1602482*x^30 + 1316113*x^29 + 1114023*x^28 + 883313*x^27 + 725930*x^26 + 551915*x^25 + 439662*x^24 + 318308*x^23 + 245205*x^22 + 166823*x^21 + 124009*x^20 + 78506*x^19 + 56071*x^18 + 32361*x^17 + 22208*x^16 + 11357*x^15 + 7673*x^14 + 3221*x^13 + 2294*x^12 + 684*x^11 + 594*x^10 + 59*x^9 + 133*x^8 + 21*x^7 + 18*x^6 - 2*x^4 - 3*x^3 + 9*x^2 - 5*x + 1) divided by (see next line)

((x^20 - 1)*(x^11 - x^10 + x^6 - x^5 + x - 1)*(x^7 - 2*x^6 + x^5 + x^4 - x^3 - x^2 + 2*x - 1)*(x^4 + x^3 + x^2 + x + 1)^4*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^2 + 1)*(x^2 + 1)^5*(x^2 + x + 1)^5*(x + 1)^11*(x - 1)^22).

Crossrefs

Row 5 of A318795.

Cf. A002724, A053307, A052365, A052366.

Sequence in context: A052366 A309682 A318563 * A052372 A052373 A007716

Adjacent sequences: A052364 A052365 A052366 * A052368 A052369 A052370

Keyword

nonn

Author

Vladeta Jovovic, Mar 08 2000

Status

approved