OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (40, -726, 7990, -60079, 329634, -1376232, 4502316, -11796723, 25181344, -44394801, 65362923, -81084845, 85345726, -76614855, 58864971, -38780652, 21910044, -10597053, 4370655, -1527144, 447532, -108365, 21201, -3237, 364, -27, 1).
FORMULA
G.f.: (((1-x)^3 - x)^3 - x*(1-x)^6)^3 / ((((1-x)^3 - x)^3 - x*(1-x)^6)^3 - x*(1-x)^6*((1-x)^3 - x)^6).
a(n) = 40*a(n-1) - 726*a(n-2) + 7990*a(n-3) - 60079*a(n-4) + 329634*a(n-5) - 1376232*a(n-6) + 4502316*a(n-7) - 11796723*a(n-8) + 25181344*a(n-9) - 44394801*a(n-10) + 65362923*a(n-11) - 81084845*a(n-12) + 85345726*a(n-13) - 76614855*a(n-14) + 58864971*a(n-15) - 38780652*a(n-16) + 21910044*a(n-17) - 10597053*a(n-18) + 4370655*a(n-19) - 1527144*a(n-20) + 447532*a(n-21) - 108365*a(n-22) + 21201*a(n-23) - 3237*a(n-24) + 364*a(n-25) - 27*a(n-26) + a(n-27) for n > 27.
a(0) = 1; a(n) = Sum_{i=1..n} Sum_{j=1..i} Sum_{k=1..j} binomial(n+2*i-1,3*i-1) * binomial(i+2*j-1,3*j-1) * binomial(j+2*k-1,3*k-1).
PROG
(PARI) a(n) = if(n==0, 1, sum(i=1, n, sum(j=1, i, sum(k=1, j, binomial(n+2*i-1, 3*i-1)*binomial(i+2*j-1, 3*j-1)*binomial(j+2*k-1, 3*k-1)))));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 20 2026
STATUS
approved