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A176287 Diagonal sums of number triangle A092392. 3
1, 2, 7, 23, 81, 291, 1066, 3955, 14818, 55937, 212428, 810664, 3106167, 11942261, 46047897, 178000950, 689580319, 2676598447, 10406929687, 40525045518, 158022343991, 616950024334, 2411395005316, 9434753907065, 36948692202031 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A176288.

LINKS

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

FORMULA

G.f.: 1/(sqrt(1-4*x)*(1-x^2*c(x)) = 2/(sqrt(1-4*x)*(2-x+x*sqrt(1-4x))), c(x) the g.f. of A000108.

a(n) = Sum_{k=0..floor(n/2)} C(2n-3k,n-k).

a(n) = Sum_{k=0..n} A000984(k)*A132364(n-k).

Conjecture: 2*n*a(n) +(6-11*n)*a(n-1) +(13*n-16)*a(n-2) +2*(5-n)*a(n-3) +3*(2-3*n)*a(n-4) +2*(2*n-5)*a(n-5)=0. - R. J. Mathar, Nov 15 2012

a(n) ~ 2^(2*n+3) / (7*sqrt(Pi*n)). - Vaclav Kotesovec, Feb 04 2014

MAPLE

seq( add(binomial(2*n-3*k, n-k), k=0..floor(n/2)) , n=0..25); # G. C. Greubel, Nov 25 2019

MATHEMATICA

CoefficientList[Series[2/(Sqrt[1-4*x]*(2-x+x*Sqrt[1-4*x])), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 04 2014 *)

a[n_]:= Sum[Binomial[2*n-3*k, n-k], {k, 0, Floor[n/2]}]; Table[a[n], {n, 0, 25}] (* G. C. Greubel, Oct 19 2016 *)

PROG

(PARI) a(n) = sum(k=0, n\2, binomial(2*n-3*k, n-k)); \\ Michel Marcus, Oct 20 2016

(MAGMA) [ &+[Binomial(2*n-3*k, n-k): k in [0..Floor(n/2)]] : n in [0..25]]; // G. C. Greubel, Nov 25 2019

(Sage) [sum(binomial(2*n-3*k, n-k) for k in (0..floor(n/2))) for n in (0..25)] # G. C. Greubel, Nov 25 2019

(GAP) List([0..25], n-> Sum([0..Int(n/2)], k-> Binomial(2*n-3*k, n-k) )); # G. C. Greubel, Nov 25 2019

CROSSREFS

Cf. A000108, A000984, A092392, A132364.

Sequence in context: A130567 A091514 A143629 * A119371 A151290 A047002

Adjacent sequences:  A176284 A176285 A176286 * A176288 A176289 A176290

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 14 2010

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)