|
Search: id:A128862
|
|
|
| A128862 |
|
Numbers simultaneously triangular and centered triangular. |
|
+0
3
|
|
| 1, 10, 136, 1891, 26335, 366796, 5108806, 71156485, 991081981, 13803991246, 192264795460
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
A128862 is an essentially identical sequence. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
|
|
REFERENCES
|
S. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, submitted.
|
|
FORMULA
|
Equals (3*A001570(n) + 1)/4. - Ralf Stephan, May 20 2007
Define x(n) and y(n) by (3+sqrt(3))*(2+sqrt(3))^n = x(n) + y(n)*sqrt(3); let s(n) = (y(n)+1)/2; then a(n) = (1/2)*(2+3*(s(n)^2-s(n))).
a(n+2)=14*a(n+1)-a(n)-3, a(n+1)=7*a(n)-1.5+0.5*(192*a(n)^2-96*a(n)-15)^0.5. G.f.: f(z)=a(1)*z+a(2)*z^2+...=(z*(1-5*z+z^2))/((1-z)*(1-14*z+z^2)) - Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 01 2007
|
|
EXAMPLE
|
a(1)=10 because 10 is the third triangular number and the fourth centered triangular number
|
|
MAPLE
|
CP := n -> 1+1/2*3*(n^2-n): N:=10: u:=2: v:=1: x:=3: y:=1: k_pcp:=[1]: for i from 1 to N do tempx:=x; tempy:=y; x:=tempx*u+3*tempy*v: y:=tempx*v+tempy*u: s:=(y+1)/2: k_pcp:=[op(k_pcp), CP(s)]: end do: k_pcp;
|
|
CROSSREFS
|
Cf. A000217, A005448.
Sequence in context: A024135 A050408 A133197 this_sequence A129803 A065024 A026244
Adjacent sequences: A128859 A128860 A128861 this_sequence A128863 A128864 A128865
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Steven Schlicker (schlicks(AT)gvsu.edu), Apr 24 2007
|
|
|
Search completed in 0.002 seconds
|
