login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253475 Indices of centered square numbers (A001844) which are also centered hexagonal numbers (A003215). 3
1, 6, 55, 540, 5341, 52866, 523315, 5180280, 51279481, 507614526, 5024865775, 49741043220, 492385566421, 4874114620986, 48248760643435, 477613491813360, 4727886157490161, 46801248083088246, 463284594673392295, 4586044698650834700, 45397162391834954701 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 4*x^2 - 6*y^2 - 4*x + 6*y = 0, the corresponding values of y being A054318.

Also indices of centered hexagonal numbers (A003215) which are also hexagonal numbers (A000384).

Also indices of terms in sequence A193218 which are the square root of a sum of 5th powers (A000539). - Daniel Poveda Parrilla, Jun 10 2017

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (11,-11,1).

FORMULA

a(n) = 11*a(n-1)-11*a(n-2)+a(n-3).

G.f.: x*(5*x-1) / ((x-1)*(x^2-10*x+1)).

a(n) = sqrt((-2-(5-2*sqrt(6))^n-(5+2*sqrt(6))^n)*(2-(5-2*sqrt(6))^(1+n)-(5+2*sqrt(6))^(1+n)))/(4*sqrt(2)). - Gerry Martens, Jun 04 2015

EXAMPLE

6 is in the sequence because the 6th centered square number is 61, which is also the 5th centered hexagonal number.

PROG

(PARI) Vec(x*(5*x-1)/((x-1)*(x^2-10*x+1)) + O(x^100))

CROSSREFS

Cf. A000384, A000539, A001844, A003215, A054318, A193218, A253175.

Sequence in context: A295548 A198855 A318592 * A215853 A110431 A121661

Adjacent sequences:  A253472 A253473 A253474 * A253476 A253477 A253478

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 02 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 23 17:02 EST 2020. Contains 338590 sequences. (Running on oeis4.)