A064385 a(n) = 2*5^n - 3.

7, 47, 247, 1247, 6247, 31247, 156247, 781247, 3906247, 19531247, 97656247, 488281247, 2441406247, 12207031247, 61035156247, 305175781247, 1525878906247, 7629394531247, 38146972656247

Offset

1,1

Comments

5th 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.

Links

Harry J. Smith, Table of n, a(n) for n=1,...,100

Index entries for linear recurrences with constant coefficients, signature (6,-5).

Formula

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)

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;

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) ) } \\ Harry J. Smith, Sep 13 2009
(Magma) [2*5^n-3: n in [1..30]]; // Vincenzo Librandi, Nov 12 2011

Crossrefs

Sequence in context: A009202 A093112 A091516 * A269520 A009260 A201871

Adjacent sequences: A064382 A064383 A064384 * A064386 A064387 A064388

Keyword

nonn,easy

Author

Daniel Dockery (drd(AT)peritus.virtualave.net), Sep 16 2001

Status

approved