A164586 Row sums of generalized rhombic triangle A164585.

1, 1, 3, 8, 19, 51, 134, 354, 952, 2558, 6917, 18787, 51146, 139702, 382464, 1049221, 2883964, 7939822, 21891635, 60440322, 167068352, 462315544, 1280607173, 3550505517, 9852130198, 27359426032, 76031905038, 211433821121, 588332188162, 1638031887892

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: (1-2*x-2*x^2-x^3- sqrt(1-4*x^2-10*x^3-4*x^4+x^6))/(2*x*(x^4+3*x^3+4*x^2+x-1)).

Conjecture: (n+1)*a(n) +(n-1)*a(n-1) +2*(-2*n-1)*a(n-2) +2*(-7*n+10)*a(n-3) +14*(-n+2)*a(n-4) +2*(-2*n+3)*a(n-5) +(n-7)*a(n-6) +(n-5)*a(n-7)=0. - R. J. Mathar, Feb 10 2015

Maple

A164586 := proc(n)
    add(A164585(n, k), k=0..n) ;
end proc: # R. J. Mathar, Feb 10 2015

Mathematica

CoefficientList[Series[(1 - 2 x - 2 x^2 - x^3 - Sqrt [1 - 4 x^2 - 10 x^3 - 4 x^4 + x^6])/(2 x (x^4 + 3 x^3 + 4 x^2 + x - 1)), {x, 0, 50}], x] (* G. C. Greubel, Aug 12 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((1-2*x-2*x^2-x^3- sqrt(1-4*x^2-10*x^3-4*x^4 +x^6))/(2*x*(x^4+3*x^3+4*x^2+x-1))) \\ G. C. Greubel, Aug 12 2017

Crossrefs

Sequence in context: A339525 A295045 A181849 * A018032 A086808 A170900

Adjacent sequences: A164583 A164584 A164585 * A164587 A164588 A164589

Keyword

easy,nonn

Author

Paul Barry, Aug 17 2009

Status

approved