A285998 a(n) = Sum_{k=0..floor(n/2)} (n-k)*(k+1).

1, 4, 7, 16, 22, 40, 50, 80, 95, 140, 161, 224, 252, 336, 372, 480, 525, 660, 715, 880, 946, 1144, 1222, 1456, 1547, 1820, 1925, 2240, 2360, 2720, 2856, 3264, 3417, 3876, 4047, 4560, 4750, 5320, 5530, 6160, 6391, 7084, 7337, 8096, 8372, 9200, 9500, 10400, 10725

Offset

1,2

Links

Table of n, a(n) for n=1..49.

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

Cf. A000292 (with n instead of n/2).

Sequence in context: A067398 A325657 A054599 * A229917 A095755 A245937

Adjacent sequences: A285995 A285996 A285997 * A285999 A286000 A286001

Keyword

nonn,easy

Author

Zhandos Mambetaliyev, Jun 15 2017

Extensions

More terms from Michel Marcus, Jun 15 2017

Status

approved