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A206800 Riordan array (1/(1-3*x+x^2), x*(1-x)/(1-3*x+x^2)). 1
1, 3, 1, 8, 5, 1, 21, 19, 7, 1, 55, 65, 34, 9, 1, 144, 210, 141, 53, 11, 1, 377, 654, 534, 257, 76, 13, 1, 987, 1985, 1905, 1111, 421, 103, 15, 1, 2584, 5911, 6512, 4447, 2041, 641, 134, 17, 1, 6765, 17345, 21557, 16837, 9038, 3440, 925, 169, 19, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Subtriangle of the triangle given by (0, 3, -1/3, 1/3, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1/3, 1/3, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Antidiagonal sums are A072264(n).

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1).

G.f.: 1/(1-(y+3)*x+(y+1)*x^2).

Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n* A015587(n+1), (-1)^n*A190953(n+1), (-1)^n*A015566(n+1), (-1)*A189800(n+1), (-1)^n*A015541(n+1), (-1)^n*A085939(n+1), (-1)^n*A015523(n+1), (-1)^n*A063727(n), (-1)^n*A006130(n), A077957(n), A000045(n+1), A000079(n), A001906(n+1), A007070(n), A116415(n), A084326(n+1), A190974(n+1), A190978(n+1), A190984(n+1), A190990(n+1), A190872(n) for x = -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively.

EXAMPLE

Triangle begins :

1

3, 1

8, 5, 1

21, 19, 7, 1

55, 65, 34, 9, 1

144, 210, 141, 53, 11, 1

377, 654, 534, 257, 76, 13, 1

987, 1985, 1905, 1111, 421, 103, 15, 1

2584, 5911, 6512, 4447, 2041, 641, 134, 17, 1

6765, 17345, 21557, 16837, 9038, 3440, 925, 169, 19, 1

Triangle (0,3,-1/3,1/3,0,0,0,0,0,...) DELTA (1,0,-1/3,1/3,0,0,0,0,...) begins :

1

0, 1

0, 3, 1

0, 8, 5, 1

0, 21, 19, 7, 1

0, 55, 65, 34, 9, 1...

CROSSREFS

Cf. A000045, A001519, A001906, A001870,

Sequence in context: A016477 A172157 A209136 * A258205 A258018 A188939

Adjacent sequences:  A206797 A206798 A206799 * A206801 A206802 A206803

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Feb 12 2012

STATUS

approved

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Last modified October 21 06:24 EDT 2019. Contains 328292 sequences. (Running on oeis4.)