A162771 -id:A162771 - cp's OEIS frontend

A162963 a(n) = 5*a(n-2) for n > 2; a(1) = 2, a(2) = 5.

2, 5, 10, 25, 50, 125, 250, 625, 1250, 3125, 6250, 15625, 31250, 78125, 156250, 390625, 781250, 1953125, 3906250, 9765625, 19531250, 48828125, 97656250, 244140625, 488281250, 1220703125, 2441406250, 6103515625, 12207031250

Offset: 1

Klaus Brockhaus, Jul 19 2009

Binomial transform is A162770, second binomial transform is A001077 without initial 1, third binomial transform is A162771, fourth binomial transform is A162772, fifth binomial transform is A162773.

Index entries for linear recurrences with constant coefficients, signature (0,5).

Cf. A000351 (powers of 5), A026383, A001077, A162770, A162771, A162772, A162773.

[ n le 2 select 3*n-1 else 5*Self(n-2): n in [1..29] ];

a(n) = (3-(-1)^n)*5^(1/4*(2*n-1+(-1)^n))/2.
G.f.: x*(2+5*x)/(1-5*x^2).
a(n) = A026383(n) for n >= 1.

A162772 a(n) = ((2+sqrt(5))(4+sqrt(5))^n + (2-sqrt(5))(4-sqrt(5))^n)/2.

Original entry on oeis.org

2, 13, 82, 513, 3202, 19973, 124562, 776793, 4844162, 30208573, 188382802, 1174768113, 7325934082, 45685023413, 284894912402, 1776624041673, 11079148296962, 69090321917293, 430851944071762, 2686822011483873

Offset: 0

Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009

nonn

Binomial transform of A162771. Fourth binomial transform of A162963. Inverse binomial transform of A162773.

Index entries for linear recurrences with constant coefficients, signature (8, -11).

Cf. A162771, A162963, A162773.

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((2+r)*(4+r)^n+(2-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 19 2009

a(n) = 8*a(n-1) - 11*a(n-1) for n > 1; a(0) = 2, a(1) = 13.

G.f.: (2-3*x)/(1-8*x+11*x^2).

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 19 2009

cp's OEIS Frontend

A162963 a(n) = 5*a(n-2) for n > 2; a(1) = 2, a(2) = 5.

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A162772 a(n) = ((2+sqrt(5))(4+sqrt(5))^n + (2-sqrt(5))(4-sqrt(5))^n)/2.

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cp's OEIS Frontend

A162963 a(n) = 5*a(n-2) for n > 2; a(1) = 2, a(2) = 5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Formula

A162772 a(n) = ((2+sqrt(5))*(4+sqrt(5))^n + (2-sqrt(5))*(4-sqrt(5))^n)/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Formula

Extensions

A162772 a(n) = ((2+sqrt(5))(4+sqrt(5))^n + (2-sqrt(5))(4-sqrt(5))^n)/2.