login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
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 o.g.f. 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 A351293

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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 11:16 EST 2022. Contains 358396 sequences. (Running on oeis4.)