A159380 Number of n X n arrays of squares of integers with every (n-1) X (n-1) subblock summing to 10.

46, 8780, 2360696, 350007360, 30587815086, 1354835948116, 33260056683980, 522276436822144, 5839731483074618, 50097272262566248, 347612897548180792, 2027444729799605536, 10230660755186873586, 45666006349045615904

Offset

3,1

Links

R. H. Hardin, Table of n, a(n) for n=3..23

Index entries for linear recurrences with constant coefficients, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).

Formula

a(n) = (936533802*n^20 - 36001207145*n^19 + 622792384955*n^18 - 6253364338440*n^17 + 37851028746252*n^16 - 106861751384070*n^15 - 361406279253990*n^14 + 6020646293099020*n^13 - 37914859899827818*n^12 + 159323939501288055*n^11 - 496896470881581885*n^10 + 1194661749864039780*n^9 - 2250923413670955828*n^8 + 3355424999095241680*n^7 - 4007305827926228080*n^6 + 3935810505847400640*n^5 - 3314069608404201408*n^4 + 2445300834249876480*n^3 - 1484282086246656000*n^2 + 622984191911424000*n - 128034305925120000)/1646023680000. - Robert Israel, Dec 20 2023

Maple

G:= proc(s, m)
   option remember; local t;
   if s >= 9 then t:=  expand(m!/((s-9)!*(m-(s-9)-1)!)) else t:= 0 fi; # 9, 1* 0*
   if s >= 8 then t:= t + expand(m!/(2*(s-8)!*(m-(s-8)-2)!)) fi; # 4, 4, 1*, 0&*
   if s >= 4 then t:= t + expand(m!/(s-4)!/(m-(s-4)-1)!) fi; # 4, 1*, 0*
   t + expand(m!/(s!*(m-s)!)); # 1*, 0*
end proc:
t:= 0:
for a in [0, 1, 4, 9] do
 for c in [0, 1, 4, 9] do
    for b from 0 to 10 - max(a, c) do
      for d from 0 to 10 - a - b do
        e:= 10 - a - b - d;
        f:= 10 - b - c - e;
        if f < 0 then next fi;
        for g in [0, 1, 4, 9] do
          h:= 10 - d - e - g;
          if h < 0 then next fi;
          i:= 10 - e - f - h;
          if not member(i, [0, 1, 4, 9]) then next fi;
          t:= t + G(b, n-2) * G(d, n-2) * G(f, n-2) * G(h, n-2) * G(e, (n-2)^2)
od od od od od:
Q:= normal(t):
seq(Q, n=3 .. 25); # Robert Israel, Dec 20 2023

Crossrefs

Cf. A159376, A159379.

Sequence in context: A223891 A243648 A302114 * A134793 A177639 A222097

Adjacent sequences: A159377 A159378 A159379 * A159381 A159382 A159383

Keyword

nonn

Author

R. H. Hardin, Apr 11 2009

Status

approved