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A144404 A symmetrical triangle read by rows: t(n,m) = 3*binomial[n, m]^2 - binomial[n, m] - 1. 0
1, 1, 1, 1, 9, 1, 1, 23, 23, 1, 1, 43, 101, 43, 1, 1, 69, 289, 289, 69, 1, 1, 101, 659, 1179, 659, 101, 1, 1, 139, 1301, 3639, 3639, 1301, 139, 1, 1, 183, 2323, 9351, 14629, 9351, 2323, 183, 1, 1, 233, 3851, 21083, 47501, 47501, 21083, 3851, 233, 1, 1, 289, 6029 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are 1, 2, 11, 48, 189, 718, 2701, 10160, 38345, 145338, 553233, ...

LINKS

Table of n, a(n) for n=0..57.

FORMULA

From Robert Israel, Jul 11 2016: (Start)

t(n,m) = A144390(A007318(n,m)) = 3*A008459(n,m) - A007318(n,m).

Row sums: 3*binomial(2*n,n) - 2^n - n - 1.

Generating function as triangle: g(x,y) = 3/sqrt(1-2*x-2*x*y+x^2-2*x^2*y+x^2*y^2) - 1/(1-x-x*y)+1/((1-x)*(1-x*y)). (End)

EXAMPLE

{1},

{1, 1},

{1, 9, 1},

{1, 23, 23, 1},

{1, 43, 101, 43, 1},

{1, 69, 289, 289, 69, 1},

{1, 101, 659, 1179, 659, 101, 1},

{1, 139, 1301, 3639, 3639, 1301, 139, 1},

{1, 183, 2323, 9351, 14629, 9351, 2323, 183, 1},

{1, 233, 3851, 21083, 47501, 47501, 21083, 3851, 233, 1},

{1, 289, 6029, 43079, 132089, 190259, 132089, 43079, 6029, 289, 1}

MAPLE

T:= (n, m) -> 3*Binomial(n, m)^2 - Binomial(n, m)-1:

seq(seq(T(n, m), m=0..n), n=0..10); # Robert Israel, Jul 11 2016

MATHEMATICA

Table[Table[3*Binomial[n, m]^2 - Binomial[n, m] - 1, {m, 0, n}], {n, 0, 10}]; Flatten[%]

CROSSREFS

Cf. A007318, A008459, A144390.

Sequence in context: A143681 A081582 A174346 * A014761 A073702 A171822

Adjacent sequences:  A144401 A144402 A144403 * A144405 A144406 A144407

KEYWORD

nonn

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 03 2008

EXTENSIONS

Offset changed by Robert Israel, Jul 11 2016

STATUS

approved

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Last modified August 25 03:55 EDT 2019. Contains 326318 sequences. (Running on oeis4.)