OFFSET
3,1
LINKS
R. H. Hardin, Table of n, a(n) for n = 3..27
Index entries for linear recurrences with constant coefficients, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).
FORMULA
a(n) = (213086953*n^18 - 7234157232*n^17 + 109387042419*n^16 - 944291714616*n^15 + 4732047974274*n^14 - 8876879623584*n^13 - 60234921458282*n^12 + 630926806905936*n^11 - 3155566369823715*n^10 + 10733292326883024*n^9 - 26950021111932873*n^8 + 51435177242228136*n^7 - 75424820511654584*n^6 + 85302351200676672*n^5 - 74679591278805264*n^4 + 50936307964412544*n^3 - 26904530479120128*n^2 + 10180065773445120*n - 2048904435916800)/65840947200. - Robert Israel, Dec 19 2023
MAPLE
G:= proc(s, m)
option remember; local t;
if s = 9 then t:= m else t:= 0 fi; # 9, 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 9 - max(a, c) do
for d from 0 to 9 - a - b do
e:= 9 - a - b - d;
f:= 9 - b - c - e;
if f < 0 then next fi;
for g in [0, 1, 4, 9] do
h:= 9 - d - e - g;
if h < 0 then next fi;
i:= 9 - 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..30); # Robert Israel, Dec 19 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Apr 11 2009
STATUS
approved