login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144404 Triangle T(n,k) = 3*binomial(n, k)^2 - binomial(n, k) - 1, read by rows. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

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.

G.f. 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

Triangle begins as:

  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[3*Binomial[n, k]^2 -Binomial[n, k] -1, {n, 0, 12}, {k, 0, n}]//Flatten

PROG

(Magma) [3*Binomial(n, k)^2 -Binomial(n, k) -1: k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 27 2021

(Sage) flatten([[3*binomial(n, k)^2 -binomial(n, k) -1 for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 27 2021

CROSSREFS

Cf. A000984, A007318, A008459, A144390, A144405.

Sequence in context: A143681 A081582 A174346 * A014761 A073702 A171822

Adjacent sequences:  A144401 A144402 A144403 * A144405 A144406 A144407

KEYWORD

nonn,tabl

AUTHOR

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

EXTENSIONS

Offset changed by Robert Israel, Jul 11 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 16:57 EDT 2021. Contains 345417 sequences. (Running on oeis4.)