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

0,2

Links

Table of n, a(n) for n=0..28.

N. J. A. Sloane, Transforms

Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-1,1).

Formula

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

Example

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

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 *)

Crossrefs

Cf. A008805.

Sequence in context: A269506 A292816 A105635 * A297187 A231509 A318018

Adjacent sequences: A178317 A178318 A178319 * A178321 A178322 A178323

Keyword

nonn,easy

Author

Gary W. Adamson, Dec 21 2010

Extensions

Edited by Alois P. Heinz, Dec 25 2010

Status

approved