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7, 47, 247, 1247, 6247, 31247, 156247, 781247, 3906247, 19531247, 97656247, 488281247, 2441406247, 12207031247, 61035156247, 305175781247, 1525878906247, 7629394531247, 38146972656247
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 5-th polygonal numbers for polygons of 5^n sides divided by 5: p(5,5^x)/5, where p(n,k)=(n/2)*(n*k-k+4-2*n).
This sequence exhibits periodic digit repetition; e.g. the last digit repeats as 7, the penultimate as 4 and the antepenultimate as 2, all with a period of 1; the fourth-to-last digit repeats the sequence 1, 6 with a period of 2; the fifth-to-last repeats the sequence 3, 5, 8, 0; the sixth-to-last repeats 1, 7, 9, 5, 6, 2, 4, 0. And so on, it seems, for the other digits as the numbers grow.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,100
Index to sequences with linear recurrences with constant coefficients, signature (6,-5).
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FORMULA
| Contribution from Vincenzo Librandi, Nov 12 2011 (Start)
a(n) = 5*a(n-1)+12.
a(n) = 6*a(n-1)-5*a(n-2).
G.f.: (2-5*x+15*x^2)/((1-x)*(1-5*x)).
(End)
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MAPLE
| p := proc(n, k) (n/2)*(n*k-k+4-2*n) end: for x from 1 to 19 do p(5, 5^x)/5 od; q := proc(x) 2*5^x-3 end: for x from 1 to 19 do q(x) od;
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PROG
| (PARI) p(n, k) = (n/2)*(n*k-k+4-2*n) for(x=1, 19, print(p(5, 5^x)/5)) q(x) = 2*5^x-3 for(x=1, 19, print(q(x)))
(PARI) { for (n=1, 100, write("b064385.txt", n, " ", 2*5^n - 3) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 13 2009]
(MAGMA) [2*5^n-3: n in [1..30]]; // Vincenzo Librandi, Nov 12 2011
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CROSSREFS
| Sequence in context: A009202 A093112 A091516 * A009260 A201871 A198845
Adjacent sequences: A064382 A064383 A064384 * A064386 A064387 A064388
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KEYWORD
| nonn,easy
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AUTHOR
| Daniel Dockery (drd(AT)peritus.virtualave.net), Sep 16, 2001
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