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!)
A103219 Triangle read by rows: T(n,k) = (n+1-k)*(4*(n+1-k)^2 - 1)/3+2*k*(n+1-k)^2. 2

%I

%S 1,10,3,35,18,5,84,53,26,7,165,116,71,34,9,286,215,148,89,42,11,455,

%T 358,265,180,107,50,13,680,553,430,315,212,125,58,15,969,808,651,502,

%U 365,244,143,66,17,1330,1131,936,749,574,415,276,161,74,19,1771,1530,1293

%N Triangle read by rows: T(n,k) = (n+1-k)*(4*(n+1-k)^2 - 1)/3+2*k*(n+1-k)^2.

%C The triangle is generated from the product B * A of the infinite lower triangular matrices A =

%C 1 0 0 0...

%C 3 1 0 0...

%C 5 3 1 0...

%C 7 5 3 1...

%C ...

%C and B =

%C 1 0 0 0...

%C 1 3 0 0...

%C 1 3 5 0...

%C 1 3 5 7...

%C ...

%e Triangle begins:

%e 1,

%e 10,3,

%e 35,18,5,

%e 84,53,26,7,

%e 165,116,71,34,9,

%e 286,215,148,89,42,11,

%t T[n_, k_] := (n + 1 - k)*(4*(n + 1 - k)^2 - 1)/3 + 2*k*(n + 1 - k)^2; Flatten[ Table[ T[n, k], {n, 0, 10}, {k, 0, n}]] (* _Robert G. Wilson v_, Feb 10 2005 *)

%o (PARI) T(n,k)=(n+1-k)*(4*(n+1-k)^2-1)/3+2*k*(n+1-k)^2; for(i=0,10, for(j=0,i,print1(T(i,j),","));print())

%Y Row sums give A103220.

%Y T(n, 0 = n*(4*n^2 - 1)/3 = A000447(n+1);

%Y T(n+1, n)= 8*n+2 = A017089(n+1);

%Y Cf. A103218 (for product A*B), A103220.

%K nonn,tabl

%O 0,2

%A Lambert Klasen (lambert.klasen(AT)gmx.de) and _Gary W. Adamson_, Jan 26 2005

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 February 18 09:15 EST 2020. Contains 332011 sequences. (Running on oeis4.)