OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
G.f.: x * (1+3*x)/((1-x)^4*(1+x)^3). - Joerg Arndt, Jun 25 2017
a(n) = 1/16 + 13*n/24 + 7*n^2/16 + n^3/12 + (-1)^n*(-1/16 + n/8 + n^2/16). - Vaclav Kotesovec, Jun 25 2017
E.g.f.: (x*(21 + 18*x + 2*x^2)*cosh(x) + (3 + 30*x + 15*x^2 + 2*x^3)*sinh(x))/24. - Stefano Spezia, Dec 23 2022
EXAMPLE
a(2) = (2*1)+(1*2) = 4.
a(3) = (3*1)+(2*2) = 7.
a(4) = (4*1)+(3*2)+(2*3) = 16.
a(5) = (5*1)+(4*2)+(3*3) = 22.
MATHEMATICA
Table[Sum[(n - k) (k + 1), {k, 0, Floor[n/2]}], {n, 49}] (* Michael De Vlieger, Jun 23 2017 *)
PROG
(PARI) a(n) = sum(k=0, n\2, (n-k)*(k+1)); \\ Michel Marcus, Jun 15 2017
(PARI) a(n) = my(r = n%2, n = (n + 4)>>1); 4 * binomial(n, 3) + r * binomial(n, 2); \\ David A. Corneth, Jun 23 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zhandos Mambetaliyev, Jun 15 2017
EXTENSIONS
More terms from Michel Marcus, Jun 15 2017
STATUS
approved