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Search: id:A128919
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| A128919 |
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Numbers simultaneously heptagonal and centered heptagonal. |
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+0
3
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| 1, 148, 21022, 2984983, 423846571, 60183228106, 8545594544488, 1213414242089197, 172296276782121493, 24464857888819162816, 3473837523935538998386
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, submitted.
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FORMULA
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x(n) + y(n)*sqrt(35) = (7+sqrt(35))*(6+sqrt(35))^n s(n) = (y(n)+1)/2 a(n) = (1/2)*(2+7*(s(n)^2-s(n)))
a(n+2)=142*a(n+1)-a(n)+7, a(n+1)=71*a(n)+3.5+1.5*(2240*a(n)^2+224*a(n)-63)^0.5. G.f.: f(z)=a(1)*z+a(2)*z^2+...=((z*(1+5*z+z^2))/((1-z)*(1-142*z+z^2)) - Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 01 2007
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EXAMPLE
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a(1)=148 because 148 is the seventh centered heptagonal number and the eighth heptagonal number.
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MAPLE
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CP := n -> 1+1/2*7*(n^2-n): N:=10: u:=6: v:=1: x:=7: y:=1: k_pcp:=[1]: for i from 1 to N do tempx:=x; tempy:=y; x:=tempx*u+35*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
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Cf. A000566, A069099.
Adjacent sequences: A128916 A128917 A128918 this_sequence A128920 A128921 A128922
Sequence in context: A127028 A121280 A035822 this_sequence A100723 A031929 A115231
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KEYWORD
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easy,nonn
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AUTHOR
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Steven Schlicker (schlicks(AT)gvsu.edu), Apr 24 2007
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