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A164586 Row sums of generalized rhombic triangle A164585. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 17 2009
STATUS
approved

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Last modified March 1 22:23 EST 2024. Contains 370443 sequences. (Running on oeis4.)