|
|
A084265
|
|
a(n) = (n^2 + 3*n + 1 + (-1)^n) / 2.
|
|
9
|
|
|
1, 2, 6, 9, 15, 20, 28, 35, 45, 54, 66, 77, 91, 104, 120, 135, 153, 170, 190, 209, 231, 252, 276, 299, 325, 350, 378, 405, 435, 464, 496, 527, 561, 594, 630, 665, 703, 740, 780, 819, 861, 902, 946, 989, 1035, 1080, 1128, 1175, 1225, 1274, 1326, 1377, 1431, 1484
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Previous name was: Modified triangular numbers.
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: cosh(x) + exp(x)*(2x+x^2/2).
a(n) = (n^2+3*n+1)/2+(-1)^n/2.
G.f.: ( -1-2*x^2+x^3 ) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Nov 26 2012
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4).
a(n) = Sum_{i=0..n+1} i-(-1)^i. (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
CoefficientList[Series[(-1 - 2 x^2 + x^3) / ((1 + x) (x - 1)^3), {x, 0, 60}], x] (* Vincenzo Librandi, Aug 15 2013 *)
|
|
PROG
|
(PARI) vector(100, n, (n^2+n-1-(-1)^n)/2) \\ Derek Orr, Mar 22 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|