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Row sums of triangle A060556.
7

%I #26 Aug 04 2021 21:01:23

%S 1,3,10,33,108,352,1145,3721,12087,39254,127469,413908,1343980,

%T 4363921,14169633,46008619,149389218,485064009,1574993356,5113971944,

%U 16604963593,53915979657,175064088671

%N Row sums of triangle A060556.

%C Equals the INVERT transform of A045623: (1, 2, 5, 12, 28, ...). - _Gary W. Adamson_, Oct 26 2010

%H Harry J. Smith, <a href="/A060557/b060557.txt">Table of n, a(n) for n = 0..500</a>

%H Nachum Dershowitz, <a href="https://arxiv.org/abs/2006.06516">Between Broadway and the Hudson: A Bijection of Corridor Paths</a>, arXiv:2006.06516 [math.CO], 2020.

%H László Németh and László Szalay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Nemeth/nemeth8.html">Sequences Involving Square Zig-Zag Shapes</a>, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5, -6, 1).

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

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

%F a(n) = 5a(n-1) - 6a(n-2) + a(n-3). - _Floor van Lamoen_, Nov 02 2005

%t 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_ *)

%t LinearRecurrence[{5,-6,1},{1,3,10},30] (* _Harvey P. Dale_, Nov 29 2013 *)

%o (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

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

%Y Cf. A053975.

%Y Cf. A052975 (row sums of triangle A060102).

%Y Cf. A045623. - _Gary W. Adamson_, Oct 26 2010

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Apr 06 2001