A060557 Row sums of triangle A060556.

1, 3, 10, 33, 108, 352, 1145, 3721, 12087, 39254, 127469, 413908, 1343980, 4363921, 14169633, 46008619, 149389218, 485064009, 1574993356, 5113971944, 16604963593, 53915979657, 175064088671

Offset: 0

Author

Wolfdieter Lang, Apr 06 2001

Keywords

• nonn
• easy

Comments

Equals the INVERT transform of A045623: (1, 2, 5, 12, 28, ...). - Gary W. Adamson, Oct 26 2010

Links

• Harry J. Smith, Table of n, a(n) for n = 0..500
• Nachum Dershowitz, Between Broadway and the Hudson: A Bijection of Corridor Paths, arXiv:2006.06516 [math.CO], 2020.
• László Németh and László Szalay, Sequences Involving Square Zig-Zag Shapes, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
• Index entries for linear recurrences with constant coefficients, signature (5, -6, 1).

Crossrefs

a(n)=A028495(2n+1).

Cf. A053975.

Cf. A052975 (row sums of triangle A060102).

Cf. A045623. - Gary W. Adamson, Oct 26 2010

Programs

Mathematica

a[0] = 1; a[1] = 3; a[2] = 10; a[n_] := a[n] = 5*a[n-1] - 6*a[n-2] + a[n-3]; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jul 05 2013, after Floor van Lamoen *)
LinearRecurrence[{5,-6,1},{1,3,10},30] (* Harvey P. Dale, Nov 29 2013 *)

PARI

{ f="b060557.txt"; a0=1; a1=3; a2=10; write(f, "0 1"); write(f, "1 3"); write(f, "2 10"); for (n=3, 500, write(f, n, " ", a=5*a2 - 6*a1 + a0); a0=a1; a1=a2; a2=a; ) } \\ Harry J. Smith, Jul 07 2009

Formula

a(n) = Sum_{m=0..n} A060556(n, m).

G.f.: (1-x)^2/(1 - 5*x + 6*x^2 - x^3).

a(n) = 5a(n-1) - 6a(n-2) + a(n-3). - Floor van Lamoen, Nov 02 2005