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A178320
INVERT transform of A008805 (triangular numbers repeated).
0
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
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
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 21 2010
EXTENSIONS
Edited by Alois P. Heinz, Dec 25 2010
STATUS
approved