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A128862
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Numbers simultaneously triangular and centered triangular.
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2
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1, 10, 136, 1891, 26335, 366796, 5108806, 71156485, 991081981, 13803991246, 192264795460
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A129803 is an essentially identical sequence. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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REFERENCES
| S. C. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, Mathematics Magazine, Vol. 84, No. 5, December 2011
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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
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EXAMPLE
| a(1)=10 because 10 is the third triangular number and the fourth centered triangular number
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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;
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CROSSREFS
| Cf. A000217, A005448.
Sequence in context: A024135 A050408 A133197 * A129803 A065024 A026244
Adjacent sequences: A128859 A128860 A128861 * A128863 A128864 A128865
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KEYWORD
| easy,nonn
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AUTHOR
| Steven Schlicker (schlicks(AT)gvsu.edu), Apr 24 2007
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EXTENSIONS
| Corrected A-number in comment - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 05 2010
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