A143061 Triangle read by rows, A000012 * A127647 * A000012.

1, 1, 2, 2, 3, 4, 3, 5, 6, 7, 5, 8, 10, 11, 12, 8, 13, 16, 18, 19, 20, 13, 21, 26, 29, 31, 32, 33, 21, 34, 42, 47, 50, 52, 53, 54, 34, 55, 68, 76, 81, 84, 86, 87, 88, 55, 89, 110, 123, 131, 136, 139, 141, 142, 143, 89, 144, 178, 199, 212, 220, 225, 228, 230, 231

Offset

1,3

Comments

Row sums = A014286 (1, 3, 9, 21, 46, 94, ...); left border = Fibonacci numbers.

Links

Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)

Formula

From Robert Israel, Nov 06 2016: (Start)

T(n,k) = A000045(n+2) - A000045(n+2-k) for 1 <= k <= n.

G.f. as triangle: x*y*(1+x^2*y)/((1-x*y)*(1-x-x^2)*(1-x*y-x^2*y^2)). (End)

Example

First few rows of the triangle are:
  1;
  1,  2;
  2,  3,  4;
  3,  5,  6,  7;
  5,  8, 10, 11, 12;
  8, 13, 16, 18, 19, 20;
  ...

Maple

seq(seq(combinat:-fibonacci(i+2)-combinat:-fibonacci(i+2-j), j=1..i), i=1..20); # Robert Israel, Nov 06 2016

Crossrefs

Cf. A000012, A000045, A014286, A127647.

Sequence in context: A146985 A132993 A106408 * A096858 A037254 A316939

Adjacent sequences: A143058 A143059 A143060 * A143062 A143063 A143064

Keyword

nonn,tabl

Author

Gary W. Adamson, Jul 20 2008

Extensions

Corrected by Dintle N Kagiso, Nov 06 2016

Status

approved