OFFSET
0,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Tenner, Bridget Eileen Reduced word manipulation: patterns and enumeration, J. Algebr. Comb. 46, No. 1, 189-217 (2017), w in S_n(231): l(w)=4.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: x*(2*x^2-3*x+2)/(1-x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = (1/6)*Sum_{i=1..n} (n-i)*((n-i)^2+11), for n >= 1.
EXAMPLE
a(1) = 2; a(2)= 5+2 = 7; a(3) = 10+5+2 = 17; a(4) = 18+10+5+2 = 35; a(5) = 30+18+10+5+2 = 65; a(6) = 47+30+18+10+5+2 = 112.
MAPLE
seq(coeff(series(x*(2*x^2-3*x+2)/(1-x)^5, x, n+1), x, n), n=0..30); # Muniru A Asiru, Aug 15 2018
PROG
(GAP) List([0..30], n->n*(n+1)*(n^2+n+22)/24); # Muniru A Asiru, Aug 15 2018
(PARI) a(n) = n*(n+1)*(n^2+n+22)/24; \\ Michel Marcus, Aug 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luce ETIENNE, Aug 14 2018
STATUS
approved