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A046196
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Indices of square numbers which are also heptagonal.
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4
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1, 9, 77, 1519, 12987, 111035, 2190397, 18727245, 160112393, 3158550955, 27004674303, 230881959671, 4554628286713, 38940721617681, 332931625733189, 6567770830889191, 56152493568021699
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.de), May 01 2009: (Start)
a(n+6)=1442*a(n+3)-a(n) with
a(-2)=-77; a(-1)=-9; a(0)=-1; a(1)=1; a(2)=9; a(3)=77;
A=(721+sqrt(10)*228)^k; B=(721-sqrt(10)*228)^k;
a(3*k+1)=(7*(A-B)/sqrt(10)+2*(A+B))/4;
a(3*k+2)=(57*(A-B)/sqrt(10)+18*(A+B))/4;
a(3*k)=(7*(A-B)/sqrt(10)-2*(A+B))/4;
(End)
GF: x * (1 + x) * (1 + 8*x + 69*x^2 + 8*x^3 + x^4) / (1-1442*x^3 + x^6). - Ant King, Nov 11 2011
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MAPLE
| Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.de), May 01 2009: (Start)
for n from 1 to 10000 do m:=sqrt((5*n*n-3*n)/2):
if (trunc(m)=m) then print(n, m): end if: end do:
(End)
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MATHEMATICA
| LinearRecurrence[{ 0, 0, 1442, 0, 0, -1 } , {1, 9, 77, 1519, 12987, 111035 }, 17] (* Ant King, Nov 11 2011 *)
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CROSSREFS
| Cf. A036354, A046195.
A046196 [From Weisenhorn Paul (paulweisenhorn(AT)online.de), May 01 2009]
Sequence in context: A046150 A124131 A000445 * A190980 A123918 A044577
Adjacent sequences: A046193 A046194 A046195 * A046197 A046198 A046199
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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