A134465 Row sums of triangle A134464.

1, 6, 16, 32, 55, 86, 126, 176, 237, 310, 396, 496, 611, 742, 890, 1056, 1241, 1446, 1672, 1920, 2191, 2486, 2806, 3152, 3525, 3926, 4356, 4816, 5307, 5830, 6386, 6976, 7601, 8262, 8960, 9696, 10471, 11286, 12142, 13040, 13981, 14966

Offset: 1

Author

Gary W. Adamson, Oct 26 2007

Keywords

• nonn
• easy

Comments

a(n) is the number of compositions of n+9 into n parts avoiding parts 2 and 3. - Milan Janjic, Jan 07 2016

Examples

			a(4) = 32 = sum of row 4, triangle A134464: (4 + 6 + 9 + 13).
a(4) = 32 = (1, 3, 3, 1) dot (1, 5, 5, 1) = (1 + 15 + 15 + 1).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, Pattern Avoiding Linear Extensions of Rectangular Posets, arXiv:1605.06825 [math.CO], 2016.
• Colin Defant, Proofs of Conjectures about Pattern-Avoiding Linear Extensions, arXiv:1905.02309 [math.CO], 2019.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A134464.

Programs

GAP

a:=[1,6,16,32];; for n in [5..50] do a[n]:=4*a[n-1]-6*a[n-2]+ 4*a[n-3]-a[n-4]; od; a; # G. C. Greubel, May 08 2019

Magma

I:=[1, 6, 16, 32]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012

Mathematica

CoefficientList[Series[(1+2*x-2*x^2)/(1-x)^4,{x,0,50}],x] (* Vincenzo Librandi, Jun 29 2012 *)

PARI

Vec(x*(1+2*x-2*x^2)/(1-x)^4 + O(x^50)) \\ Altug Alkan, Jan 07 2016

Sage

((1+2*x-2*x^2)/(1-x)^4).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, May 08 2019

Formula

Binomial transform of [1, 5, 5, 1, 0, 0, 0, ...].

G.f.: x*(1+2*x-2*x^2) / (1-x)^4. - R. J. Mathar, Apr 04 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 29 2012