OFFSET
0,2
COMMENTS
The sequence can be generated in the following way:
--------------------------- --------------------------
[0] [1] [2] [3] [4] ... [i]
--------------------------- --------------------------
[0] 1, 1, 1, 1, 1, ... t(0,i) = 1
[1] 7, 6, 5, 4, 3, ... t(1,i) = t(1,i-1) - t(0,i)
[2] 19, 13, 8, 4, 1, ... t(2,i) = t(2,i-1) - t(1,i)
[3] 37, 24, 16, 12, 11, ... t(3,i) = t(3,i-1) - t(2,i)
[4] 61, 37, 21, 9, -2, ... t(4,i) = t(4,i-1) - t(3,i)
[5] 91, 54, 33, 24, 26, ... etc.
[6] 127, 73, 40, 16, -10, ...
[7] 169, 96, 56, 40, 50, ...
[8] 217, 121, 65, 25, -25, ...
[9] 271, 150, 85, 60, 85, ...
...
Column 0 is A003215;
column 1 is A032528;
column 2 is A001082;
column 3 is A241496;
column 4 is this sequence.
The third differences are 16, -35, 64, -105, 160, ..., a signed variant of A077415. - R. J. Mathar, Apr 18 2014
LINKS
Index entries for linear recurrences with constant coefficients, signature (-1,3,3,-3,-3,1,1).
FORMULA
G.f.: (1 + 4*x + x^2) / ((1 - x)^3*(1 + x)^4). - R. J. Mathar, Apr 18 2014
a(n) = a(-n-5) = 1 + n*(n + 5)*(9 - (2*n + 5)*(-1)^n)/48. [Bruno Berselli, Apr 22 2014]
MATHEMATICA
Table[1 + n (n + 5) (9 - (2 n + 5) (-1)^n)/48, {n, 0, 60}] (* Bruno Berselli, Apr 22 2014 *)
CoefficientList[Series[(1+4x+x^2)/((1-x)^3(1+x)^4), {x, 0, 60}], x] (* or *) LinearRecurrence[{-1, 3, 3, -3, -3, 1, 1}, {1, 3, 1, 11, -2, 26, -10}, 60] (* Harvey P. Dale, Jan 27 2022 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Stefano Maruelli, Dec 19 2013
STATUS
approved