A241496 -id:A241496 - cp's OEIS frontend

1, 3, 1, 11, -2, 26, -10, 50, -25, 85, -49, 133, -84, 196, -132, 276, -195, 375, -275, 495, -374, 638, -494, 806, -637, 1001, -805, 1225, -1000, 1480, -1224, 1768, -1479, 2091, -1767, 2451, -2090, 2850, -2450, 3290, -2849, 3773, -3289, 4301, -3772, 4876, -4300, 5500, -4875, 6175, -5499, 6903, -6174, 7686, -6902

Offset: 0

Stefano Maruelli, Dec 19 2013

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

Index entries for linear recurrences with constant coefficients, signature (-1,3,3,-3,-3,1,1).

Cf. A077415; A058373: a(2k) = -A058373(k); A051925: a(2k+1) = A051925(k+2).

Columns of the table in Comments section: A001082, A003215, A032528.

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 *)

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]

cp's OEIS Frontend

A229834 Expansion of (1+4x+x^2) / ((1-x)^3(1+x)^4).

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