OFFSET
1,3
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
FORMULA
Empirical g.f.: x^2*(x^6-2*x^5+2*x^4-2*x^3+x^2-1) / ((x-1)^3*(x^2+1)*(x^4+1)). - Colin Barker, Aug 16 2014
a(n) = floor(1/120 n (15 n^4 + 330 n^3 + 2765 n^2 + 10482 n + 15208)/(n + 6)(n^2 + 11 n + 32)). - Ivan Neretin, May 20 2018
a(n) = floor(n*(n + 5)/8) for all n in Z. - Michael Somos, Mar 23 2023
EXAMPLE
G.f. = x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 8*x^6 + 10*x^7 + ... - Michael Somos, Mar 23 2023
MAPLE
seq(floor((1/120)*n*(15*n^4+330*n^3+2765*n^2+10482*n+15208)/((n+6)*(n^2+11*n+32))), n=1..50); # Muniru A Asiru, May 20 2018
MATHEMATICA
Table[Floor[1/120 n (15 n^4 + 330 n^3 + 2765 n^2 + 10482 n + 15208)/(n + 6)/ (n^2 + 11 n + 32)], {n, 42}] (* Ivan Neretin, May 20 2018 *)
a[ n_] := Quotient[n^2 + 5*n, 8]; (* Michael Somos, Mar 23 2023 *)
PROG
(GAP) List([1..50], n->Int((1/120)*n*(15*n^4+330*n^3+2765*n^2+10482*n+15208)/((n+6)*(n^2+11*n+32)))); # Muniru A Asiru, May 20 2018
(PARI) {a(n) = (n^2 + 5*n)\8}; /* Michael Somos, Mar 23 2023 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Missing a(1)=0 added by Ivan Neretin, May 20 2018
STATUS
approved