login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A073154 Triangle of numbers relating two sequences (A073157 and A073155). 2
1, 2, 4, 5, 9, 14, 18, 28, 38, 56, 70, 106, 131, 167, 237, 293, 433, 523, 613, 753, 1046, 1283, 1869, 2219, 2543, 2893, 3479, 4762, 5808, 8374, 9839, 11099, 12359, 13824, 16390, 22198 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..35.

FORMULA

Triangle {a(n, k), n >= 0, 0<=k<=n} defined by: a(0, 0)=1, a(n, 0)=A073157(n), a(n, n)=A073155(n+1), a(n, 0)=a(n-1, n-1) + a(n-2, n-2), a(n, k)=sum{j=0..k} A073157(j) * A073157(n-j).

G.f.: Sum_{n>=0, 0<=k<=n} a(n, k) x^n y^k = A(x*y)(A(x) - y A(x*y))/(1 - y) where A(x) = (1 - (1 - 4 x (1 + x)^2)^(1/2))/(2 x (1 + x)) is the ogf for A073157. - David Callan, Aug 16 2006

EXAMPLE

a(4,0)=a(3,3)+a(2,2)=56+14=70. a(5,2)=A073157(0)*A073157(5)+A073157(1)*A073157(4)+A073157(2)*A073157(3)= 1*293+2*70+5*18=523. Rows: {1}; {2,4}; {5,9,14}; {18,28,38,56}; {70,106,131,167,237}; {293,433,523,613,753,1046}; {1283,1869,2219,2543,2893,3479,4762};...

CROSSREFS

Cf. A073153, A073155, A073156, A073157, A073152.

Sequence in context: A162406 A129282 A073153 * A238656 A077882 A234273

Adjacent sequences:  A073151 A073152 A073153 * A073155 A073156 A073157

KEYWORD

easy,nonn,tabl

AUTHOR

Paul D. Hanna, Jul 29 2002

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 March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)