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

1,2

Comments

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

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).

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

Example

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).

Mathematica

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

Prog

(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
(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
(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

Crossrefs

Cf. A134464.

Sequence in context: A341276 A301698 A301713 * A036488 A131949 A345023

Adjacent sequences: A134462 A134463 A134464 * A134466 A134467 A134468

Keyword

nonn,easy

Author

Gary W. Adamson, Oct 26 2007

Status

approved