A178320 INVERT transform of A008805 (triangular numbers repeated).

1, 2, 6, 14, 35, 85, 208, 508, 1241, 3032, 7407, 18096, 44209, 108005, 263861, 644625, 1574849, 3847430, 9399452, 22963302, 56100424, 137055967, 334834156, 818015548, 1998450352, 4882307945, 11927707309, 29139948412, 71190260748

Offset: 0

Author

Gary W. Adamson, Dec 21 2010

Keywords

• nonn
• easy

Examples

			a(3) = 14 = (3, 3, 1, 1) * (1, 1, 2, 6) = (3 + 3 + 2 + 6).
		

Links

• N. J. A. Sloane, Transforms
• Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-1,1).

Crossrefs

Cf. A008805.

Programs

Maple

b:= proc(n) local m;
  m:= ceil((n+1)/2);
  m*(m+1)/2
end:
invtr:= proc(b)
  local a;
  a:= proc(n) option remember; local i;
        `if`(n<1, 1, add(a(n-i) *b(i-1), i=1..n+1))
  end;
end:
a:= invtr(b):
seq(a(n), n=0..30);

Mathematica

LinearRecurrence[{2, 2, -2, -1, 1}, {1, 2, 6, 14, 35}, 30] (* Jean-François Alcover, Nov 28 2020 *)

Formula

G.f.: -1/(x^5-x^4-2*x^3+2*x^2+2*x-1).

Extensions

Edited by Alois P. Heinz, Dec 25 2010