A186024 -id:A186024 - cp's OEIS frontend

A186025 a(n) = 0^n + 1 - F(n-1)^2 - F(n)^2, where F = A000045.

1, 0, -1, -4, -12, -33, -88, -232, -609, -1596, -4180, -10945, -28656, -75024, -196417, -514228, -1346268, -3524577, -9227464, -24157816, -63245985, -165580140, -433494436, -1134903169, -2971215072, -7778742048, -20365011073, -53316291172, -139583862444

Offset: 0

Paul Barry, Feb 10 2011

Row sums of number triangle A186024.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

Cf. A000045, A027941.

[0^n+1-Fibonacci(n-1)^2-Fibonacci(n)^2: n in [0..30]]; // Vincenzo Librandi, Apr 24 2015

Join[{1}, Table[0^n + 1 - Fibonacci[n - 1]^2 - Fibonacci[n]^2, {n, 30}]] (* Vincenzo Librandi, Apr 24 2015 *)
LinearRecurrence[{4,-4,1},{1,0,-1,-4},30] (* Harvey P. Dale, Dec 16 2015 *)

x='x+O('x^50); Vec((1-4*x+3*x^2-x^3)/(1-4*x+4*x^2-x^3)) \\ G. C. Greubel, Jul 24 2017

G.f.: (1-4x+3x^2-x^3)/(1-4x+4x^2-x^3) = (1-4x+3x^2-x^3)/((1-x)(1-3x+x^2)).

a(n) = -A027941(n-1), n>0. - R. J. Mathar, Mar 21 2013

More terms from Vincenzo Librandi, Apr 24 2015

A186023 Eigentriangle of triangle A085478.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 6, 4, 1, 1, 23, 15, 6, 1, 1, 106, 68, 28, 8, 1, 1, 567, 365, 145, 45, 10, 1, 1, 3434, 2215, 877, 262, 66, 12, 1, 1, 23137, 14917, 5936, 1750, 427, 91, 14, 1, 1, 171174, 110324, 43936, 13020, 3108, 648, 120, 16, 1, 1, 1376525, 887232, 353067, 104904, 25125, 5091, 933, 153, 18, 1, 1

Offset: 0

Paul Barry, Feb 10 2011

First column is A125273. Inverse of A186024. Rows sums are A125273(n)*(2-0^n).

			Triangle begins
       1;
       1,      1;
       2,      1,     1;
       6,      4,     1,     1;
      23,     15,     6,     1,    1;
     106,     68,    28,     8,    1,   1;
     567,    365,   145,    45,   10,   1,   1;
    3434,   2215,   877,   262,   66,  12,   1,  1;
   23137,  14917,  5936,  1750,  427,  91,  14,  1, 1;
  171174, 110324, 43936, 13020, 3108, 648, 120, 16, 1, 1;

Paul Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, arXiv preprint arXiv:1107.5490 [math.CO], 2011.

Cf. A125273, A186020, A186024,

cp's OEIS Frontend

A186025 a(n) = 0^n + 1 - F(n-1)^2 - F(n)^2, where F = A000045.

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